A family went to an amusement park and paid $12 for each adult and $8 for each child. A group of 15 people went to the park and it cost $140. This system of equations models this situation, where x is the number of adults and y is the number of children.

How many children were in the group?

x + y = 15

12x + 8x = 140

Yes, very good. correct equations

now simplify the second equation

12x+8y=140

undistribute the 4 in both 8 and 12

4 (3x+2y) = 140

divide both sides by 4

2x+3y=35

seconde equation

x+y=15

multiply by 2

2x+2y=30

compare

2x+3y=35

2x+2y=30

make the secondn one negative and add

2x+3y=35

-2x-2y=-30 +

0x+1y=5

y=5

subsiutte

x+y15

x+5=15

subttract 5

x=10

10 adults

5 kides