Question

In one baseball season, Peter hit twice the difference of the number of home runs Alice hit and 6. Altogether, they hit 18 home runs. How many home runs did each player hit that season? Let h represent Alice's home runs.

Answer 1

h = Alice's home runs
p = Peter's home runs

p = 2(h - 6)
p + h = 18

Simplified:
p = 2h - 12
p - 2h = -12

p + h = 18

Solve simultaneously:
p - 2h = -12 ...1
p + h = 18 ...2

1 - 2:
-3h = - 30
h = -30/-3
h = 10

Substitute into 2:
p + h = 18
p + 10 = 18
p = 18 - 10
p = 8

Therefore, Peter hit 8 home runs and Alice hit 10 homeruns.