Question

Write and solve an equation for each situation.

9.
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?

Answer 1

Peter 8 and Alice 10 home runs.

Explanation:

Let the home runs by peter be represented by "x" and the home runs of Alice be represented by "y".

Altogether the hit 18 home runs. This means sum of x and y would be 18. So we can write the equation as:

x + y = 18 Equation 1

Peter hit twice the difference of the number of home runs Alice hit and 6. Difference of the number of home runs Alice hit and 6 is y - 6 and twice of this difference would be 2(y - 6). So, we can set up the second equation as:

x = 2(y - 6) Equation 2

Substituting the value of x from Equation 2 into Equation 1, we get:

2(y - 6) + y = 18

2y - 12 + y = 18

3y = 30

y = 10

Substituting the value of y in Equation 2, we get:

x = 2(y - 6) = 2(10 - 6) = 2(4) = 8

This means, Peter hit 8 home runs and Alice hit 10 home runs.