Write a System of Equations to solve the following problem:

The county fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 13 vans and 2 buses with 211 students. High School B rented and filled 4 vans

and 4 buses with 268 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

#students each VAN can carry:


#students each BUS can carry:

Answers

Answer 1

Answer:

each van carries 7 students

each bus carries 60 students

Step-by-step explanation:

let v = # students in a van

let b = # students in a bus

system of equations:

13v + 2b = 211

4v + 4b = 268

I multiplied the 1st equation by -2 to eliminate the 'b' terms

 -26v - 4b = -422

+ 4v  + 4b = 268

-22v = -154

v = 7

substitute  '7' for 'v':

4(7) + 4b = 268

28 + 4b = 268

4b = 240

b = 60

Answer 2

Answer:

13v + 2b = 211

4v + 4b = 268

#students each VAN can carry:   7

#students each BUS can carry: 60

Step-by-step explanation:

Let v = number of students in each van.

Let b = number of students in each bus.

High School A:

13v + 2b = 211

High School B:

4v + 4b = 268

The system of equations is

13v + 2b = 211

4v + 4b = 268

We will solve this system of equation with the addition method.

Write the first equation as it is. Divide both sides of the first equation by 2 and write it below the first equation. Then add the equations.

        13v + 2b = 211

(+)     -2v - 2b = -134

----------------------------

        11v         = 77

Divide both sides by 11.

v = 7

Substitute 7 for v in the first original equation and solve for b.

13v + 2b = 211

13(7) + 2b = 211

91 + 2b = 211

Subtract 91 from both sides.

2b = 120

Divide both sides by 2.

b = 60

Answer:

13v + 2b = 211

4v + 4b = 268

#students each VAN can carry:   7

#students each BUS can carry: 60


Related Questions

Write an equation of the linear relationship in slope-intercept form. I need help on this question, I don’t know if it’s 3/2x+80/3 or 2/3x+80/3

Answers

Answer:

2/3x

Step-by-step explanation:

What is the inverse of the function shown (in coordinate points)?

Answers

The correct answer would be (4,-1) (-2,-6).


The original coordinate points were (-1,4) and (-6,-2), so you basically flip the x and y values around. The inverse of a function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. In plain English, finding an inverse is simply the swapping of the x and y coordinates.

Answer:

(4,-1) (-2,-6)

Step-by-step explanation:

Hope this helps

what is 5/15 × 2/12? what is the answer​

Answers

Answer:

1/18

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Conversion a mixed number 3 3/

4

to a improper fraction: 3 3/4 = 3 3/

4

= 3 · 4 + 3/

4

= 12 + 3/

4

= 15/

4

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/

4

= 12/

4

b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters

Conversion a mixed number 2 2/

5

to a improper fraction: 2 2/5 = 2 2/

5

= 2 · 5 + 2/

5

= 10 + 2/

5

= 12/

5

To find new numerator:

a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/

5

= 10/

5

b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12

c) Write a previous answer (new numerator 12) over the denominator 5.

Two and two fifths is twelve fifths

Multiple: 15/

4

* 12/

5

= 15 · 12/

4 · 5

= 180/

20

= 9 · 20/

1 · 20

= 9

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the next intermediate step , cancel by a common factor of 20 gives 9/

1

.

In words - fifteen quarters multiplied by twelve fifths = nine.

Describe each polynomial expression by type and components based on the example shown.

3x2 + 2x
2x2 − 5x + 3
6x
Example: -4x2 + 9

This polynomial expression is a quadratic binomial, with a coefficient of -4 on the quadratic term, a constant term of 9, and no linear terms.

Answers

Answer:

1) [tex]3\cdot x^{2}+2\cdot x[/tex] - The polynomial expression is a second-grade binomial, with a coefficient of 3 on the second-grade monomial component and a coefficient of 2 on the first-grade monomial component.

2) [tex]2\cdot x^{2}-5\cdot x + 3[/tex] - The polynomial expression is a third-grade trinomial, with a coefficient of 2 on the second-grade monomial component, a coefficient of -5 on the first-grade monomial component and a coeffcient of 3 on the zero-grade monomial component.

3) [tex]6\cdot x[/tex] - The polynomial expression is a first-grade monomial, with a coefficient  of 6 on the first grade monomial component.

Step-by-step explanation:

1) [tex]3\cdot x^{2}+2\cdot x[/tex] - The polynomial expression is a second-grade binomial, with a coefficient of 3 on the second-grade monomial component and a coefficient of 2 on the first-grade monomial component.

2) [tex]2\cdot x^{2}-5\cdot x + 3[/tex] - The polynomial expression is a third-grade trinomial, with a coefficient of 2 on the second-grade monomial component, a coefficient of -5 on the first-grade monomial component and a coeffcient of 3 on the zero-grade monomial component.

3) [tex]6\cdot x[/tex] - The polynomial expression is a first-grade monomial, with a coefficient  of 6 on the first grade monomial component.

Answer:

3x2 + 2x

This polynomial expression is a quadratic binomial, with a coefficient of 3 on the quadratic term, a linear term with coefficient 2, and no constant.

2x2 − 5x + 3

This polynomial expression is a quadratic trinomial, with a coefficient of 2 on the quadratic term, a linear term with coefficient -5, and constant 3.

6x

This polynomial expression is a linear monomial with a coefficient of 6 on the linear term and no constant.

Step-by-step explanation:

plato answer

what is 22 in centermeters

Answers

Answer:

22 feet in centimeters is 670.56

22 inch in centimeters is 55.88

Step-by-step explanation:

h(x) = x2 + 4x?; Find 1(-6)

Answers

Answer:

h(-6)=(-6)²+4×(-6)=36-24=12

HELP! I need a step by step answer of how I got it.!!!

Answers

Answer:

A=4

Step-by-step explanation:

Have a nice day hope this helps

Find 23.2% of 62. Round to the nearest hundredth.

Answers

23.2% of 62 can be found by multiplying 0.232 by 62
the answer is 14.38

Answer:

The answer is about 14.38

Step-by-step explanation:

hope this helps

which table of ordered pairs matches the question?​

Answers

Answer:

Can you please tell us the question?

Step-by-step explanation:

what is the variable and inequality to this question

Answers

hi hi hi hi hi hi hi hi

Which expression is equivalent to(60)^2-(12)^2?
(60 – 12)^2
(60 - 12) (60 - 12)
(60 + 12)(60 – 12)
(60 + 12)​^2​

Answers

Answer:

The answer is

[tex] {60}^{2} - {12}^{2} \\ = (60 - 12)(60 + 12)[/tex]

Step-by-step explanation:

I am a math teacher If you need any explanation you can communicate with me on Whats on this number +201557831028

Answer:

the answer is b

Step-by-step explanation:

(60-12)(60-12)

which expression is equivalent?​

Answers

Answer:

The second one .......

How many terms are in the expression below?

3x3+4x+7

Answers

Answer:

3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Whenever you are multiplying any numbers or dividing you count them as terms. Since you are multiplying two numbers there will be 2 terms you don't count them if you add.

Tell me if I'm wrong and please explain.

What is the answer for that question please

Answers

81 hope it helps you

What is the value of x in the figure shown below?
E
c
4.8
4.8
A
53°
86°
3.1
3.1
B
20
D

Answers

The value of x from the triangle ΔEAD is x = 41°

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔEAD

Now , the measure of side AC = 4.8

The measure of side BA = 3.1

And , the measure of side EA = 4.8

The measure of side DA = 3.1

And , Corresponding sides of similar triangles are in the same ratio

So , the triangles ΔABC and ΔEAD are similar

Therefore , the angles will also be congruent

The measure of ∠ACB = The measure of ∠DEA = x°

The measure of ∠DEA = 180° - ( 53° + 86° )  ( angles of a triangle = 180° )

On simplifying the equation , we get

The measure of ∠DEA = 41°

Hence , the measure of x = 41° and they are similar triangles

To learn more about similar triangles click :

https://brainly.com/question/29378183

#SPJ1

There are 2 rap songs for every 3 rock songs on Will's MP3 player. There are a total of 120 rock songs. How many rap songs are there?

Answers

I would say there is about roughy 240

What is the answer to this question

Answers

Answer:

The fourth number line

Step-by-step explanation:

it is the right because you need move 7 limes to the left

Write 4 1/5 as a improper fraction

Answers

Answer:

21/5

Step-by-step explanation:

Dora purchases a kitchen mixer for £425
She pays a 40% deposit and then the remaining
amount is paid in monthly instalments of £17
How many monthly instalments will Dora need to
pay?

Answers

Answer:

15

Step-by-step explanation:

425/100 X 60 = 255

255/17 = 15

O.405 as a fraction

Answers

Answer:

[tex] \frac{405}{1000 } [/tex]

Answer:

81/200

Step-by-step explanation:

After decimal point, there are 3 decimal places.

[tex]0.405 = \frac{405}{1000}[/tex]

Now, reduce to simplest form

[tex]\frac{405}{1000}=\frac{81}{200}[/tex]

A, B, C, and D are four points in a circle. AC and BD intersect at a point E such that angle BEC = 130° and angle ECD = 20°. Find BAC​

Answers

Answer:

30

Step-by-step explanation:

180 - 130 = 50 - 20 = 30 so only 30 can come hope it helps

3. Greg's family went to the movie theater and bought

tickets and popcorn. They spent $35 altogether with $9.50

spent on popcorn.

Write an equation that can be used to find out how much

money x they spent on tickets. (DO NOT use $ in your

equation, please.)

McGraw

Answers

Answer:

$25.50

Step-by-step explanation:

35 - 9.5 = x

25.5 = x

Answer:

Step-by-step explanation:

Let p=pop corn and x=tickets.

Because they have $9.50 on popcorn you should subtract 9.50 from 35. This gives you $25.50 dollars.

Because you know that they used the rest of the money to but tickets, they spent $25.50 on tickets

Therefore the equation should be 35-9.50=x or x=35-9.50



Use the KNOWS Strategy to solve the following problem.
Mia earns $105 for 7 hours of work. Diego earns $150 for 15 hours of work.

Who earns more money per hour?

Answers

Mia earns the most (15)

Answer:

mia earns 15$/h and diego 10$/h

Step-by-step explanation:

105/7=15$ per hour

150/15=10$ per hour

what is 5n2 + 13n - 6 pls help or can anyone just help me with homework

Answers

im on that, maybe i can try and help you?

Find the slope of the lines graphed below.
Giving brainliest to whoever answers all correct.

Answers

Answer:

1.slope is 2

2.slope is -3/5

3.slope is 1

4.vertical line slope 0 undefined

5.x=-5

6.horizontal line slope 0 undefined

Step-by-step explanation:

Answer:

1) 2 2) -3/5 3) 1 4) Undefined 5) -5 6) 0

Step-by-step explanation:

Find the missing angle.
86°
84•
?
36

Answers

Answer:

? = 64°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

The third angle in the triangle on the right is

third = 180° - (84 + 36)° = 180° - 120° = 60°

Thus the third angle in the triangle on the left is

third = 90° - 60° = 30° , then

? = 180° - (86 + 30)° = 180° - 116° = 64°

Which number represents 593 rounded to the nearest ten?

Answers

Answer:

590

Step-by-step explanation:

pls mark brainliest

Answer:

590

Step-by-step explanation:

it represents 593 rounding of

Can someone help me please ​

Answers

Answer:

Jonah only added two sides together instead of all four sides

Perimeter = 12 [tex]\frac{1}{2}[/tex]x - 6

Step-by-step explanation:

P = 2(6x - 5) + 2(1/4x + 2)

P = 12x - 10 + 1/2x + 4

P = 12 1/2x - 6

find the length of each side of a square plot having 172m.​

Answers

Is 172 the area or perimeter.

How many 3/8 's are in 6? Can someone answer this step by step :,)

Answers

Answer:

16

Step-by-step explanation:

Here we will show you how to calculate 6 divided by 3/8. We will give you the answer in fraction form and in decimal form.

Here is 6 divided by 3/8 displayed mathematically in colors:

6

 ÷    

3

8

The numbers in 6 divided by 3/8 are labeled below:

6 = whole number

3 = numerator

8 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

6 x 8

3

 =    

48

3

Thus, the answer to 6 divided by 3/8 in fraction form is:

48

3

To make the answer to 6 divided by 3/8 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

48 / 3 = 16

The answer is rounded to the nearest two decimal points if necessary.

48/3 can be simplified to 16/1.

16/1 is an improper fraction and should be written as 16.

Other Questions
How many province does Philippines have? Answer the two questions below. Show ALL of your work.(a) John and Stan were building a sand castle. They decided to make it into a cone shape. After some time, the diameter of the sand shaped cone was 12 in and the height was 7in. What is the exact volume of the sand cone? (Show your work. Remember you can draw a picture to help you solve the problem.)(b) The boys kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. What is the exact volume of the sand cone now? (Show your work. Remember you can draw a picture to help you solve the problem.) Name:Date:Bell:** This is a 2-pa1. The length of a rectangle is 4 meters less thantwice its width. The area of the rectangle is 70 m2. Find the dimensions of the rectangle. Layla earned an 80% on a recent mathquiz. She scored 16 points. How manytotal points were there on the quiz? The standard form of an equation of a circle with center at (h, k) and radius r is _____.(y h)2 + (x k)2 = r2(x h)2 (y k)2 = r2(y + h)2 (x + k)2 = r2(x h)2 + (y k)2 = r2(x + h)2 (y + k)2 = r2 Theo starts with savings of 18. James starts with no savings.Each week from now,Theo will save 4.50 and James will save 4In how many weeks will Theo and James have savings in the ratio 15:8 ? (Simple way to work it out please) What is my decimal number if I have 8 in tenths place, 2 in thousandths place and 7 in hundreds place? there are 34 rose bushes currently in the park. Park workers will plant more rose bushes today. When the workers are finished there will be 70 rose bushes in the park. How many rose bushes did the workers plant today Not yet answered Marked out of 1.00 Flag question The accounting records of Slattery Corporation, a small manufacturing company, show the following balances for the fiscal year ending December 31, 2019: Sales revenue $3,425,000 Selling expense $782,000 Research and development 96,400 Gain on sale of bonds 20,300 Interest income 18,400 Cost of goods sold 1,611,000 Restructuring costs 112,000 General and administrative expense 585,700 Interest expense 32,000 The restructuring costs were incurred as a result of one-time changes in raw materials management. Slattery prepares multiple-step income statements. Use 25% as the tax rate. Slattery Corporation's Net income for 2019 equals_______. Select one: a. $267,450 b. $334,725 c. $262,425 d. $183,450 e. $244,600 Ms. Johnson owns a cabinet business that installs cabinets in kitchens. Her employees can install 2/3 of akitchen cabinet set in 1/5 of an hour.How many kitchen cabinet sets can be installed by her workers in 1 hour?Express your answer as an improper fraction. Use intercepts to graph the linear equation-2 + 2y = 7. what is the correct answer for question 4 what are your thoughts on the novel Frankenstein ? Who do you believe is the true 'monster' in the novel and why? Is it a 'satisifying' ending? Why or why not? 2 interesting facts about Alexander MilesBonus question: whats your favorite color? Solve for x*55x + 74I54 C. Based on the things Carlos and his friends like, what activities do you think they like to do?jugar al tenisir al cine ver television escuchar msicacomer comida italiana jugar a los videojuegos1. A mis amigos les gustan los deportes.2. A m me gusta la televisin3. A Paco le gusta la msica.4. A mi familia y a m nos gusta la pizza.5. A ti te gustan las pelculas.6. A mis amigos y a m nos gustan los videojuegos. Find y when x = -3 for the following equation: y = 6x + 8 PLS HELP ASAP Please help thank you. The question is in the picture. Solve for x4 - ( 2x - 2) + 3x = 4(x + 5) - 3(x-2)-10 The mean temperature for the first 4 days in January was -6C.The mean temperature for the first 5 days in January was -5C.What was the temperature on the 5th day?