quick question

Question

At the pines entertainment park visitors may buy 3 rounds of golf and 2 go cart rides for $19. Another choice for visitors is to buy 5 rounds of golf and 3 go cart rides for $30.  Choose two variables to represent the two types of entertainment. Write two equations to describe the two options available to visitors. Use the equations to find the price for each round of golf and for each go cart ride.

Answer 1

let g = golf and r = rides

Here's what we know:

3g + 2r = 19

5g + 3r = 30

 

If we try to use substitution in this, we're going to end up with fractions. Let's use the elimination method to keep whole numbers, at least for now.

-3(3g + 2r = 19)
 2(5g + 3r = 30)

Becomes:

-9g -  6r = 57

10g + 6r = 60

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

g = 3

 

Now that we know golf rounds, we can find and check go cart rides:

3 * 3 + 2r = 19

9 + 2r = 19

2r = 10

r = 5

 

5 * 3 + 3 * 5 = 30

15 + 15 = 30

30 = 30