Question

In a baseball season, Peter hit twice the difference of the number of homeruns Alice hit and 6. Altogether, they hit 18 homeruns. How many homeruns did ALICE hit that season? show your work

Answer 1

By setting up an equation to represent the number of homeruns hit by Alice and Peter, it is determined that Alice hit 10 homeruns that season.

Step-by-step explanation:

To solve how many homeruns Alice hit, we can set up an equation where x represents the number of homeruns Alice hit. The problem states that Peter hit twice the difference between the number of homeruns Alice hit and 6. So, Peter's homeruns can be represented as 2(x - 6). Together, they hit 18 homeruns, which gives us the equation x + 2(x - 6) = 18.

First, distribute the 2 to the terms inside the parentheses:
x + 2x - 12 = 18.

Next, combine the like terms for x:
3x - 12 = 18.

Then, add 12 to both sides of the equation:
3x = 30.

Finally, divide both sides of the equation by 3 to solve for x:
x = 10.

Therefore, Alice hit 10 homeruns that season.