Question

An amusement park charges admission plus a fee for each ride. Admission plus 2 rides costs $10. Admission plus five rides costs $16. What is the charge for admission? For each ride?

Answer 1

To find the charge for admission and for each ride, we can set up a system of equations and solve them using the method of substitution. The charge for admission is $6 and the charge for each ride is $2.

Step-by-step explanation:

To find the charge for admission and for each ride, we can set up a system of equations. Let's say the charge for admission is A and the charge for each ride is R. With the given information, we can write the following equations:

A + 2R = 10 (equation 1)

A + 5R = 16 (equation 2)

To solve these equations, we can use the method of substitution. We can solve equation 1 for A and substitute it into equation 2:

A = 10 - 2R (equation 3)

Substituting equation 3 into equation 2, we get:

10 - 2R + 5R = 16

By combining like terms, we have:

3R = 6

Dividing both sides by 3, we find:

R = 2

Substituting R = 2 into equation 1, we can solve for A:

A + 2(2) = 10

A + 4 = 10

A = 6

Therefore, the charge for admission is $6 and the charge for each ride is $2.

Answer 2

The charge for admission is $6 and the charge for each ride is $2

Step-by-step explanation:

Let

x ----> the charge for admission

y ----> the charge for each ride

we have that

`x+2y=10` -----> equation A

`x+5y=16` -----> equation B

Solve the system by elimination

Subtract equation B from equation A

`x+2y=10\\-(x+5y)=-16\\---------\\2y-5y=10-16\\-3y=-6\\y=2`

Find the value of x

substitute the value of y in any equation

`x+2(2)=10`

`x+4=10`

`x=10-4`

`x=6`

therefore

The charge for admission is $6 and the charge for each ride is $2