Question

Write and solve an equation for this situation. In one baseball season, Peter hit twice the difference between the number of home runs Alice hit and 3. Altogether, they hit 9 home runs. How many home runs did each player hit that season? Let h represent Alice's home runs. Alice hit home runs. Peter hit home runs.

Answer 1

Y=8

Explanation:

The difference between the number Alice hit and 6 is X - 6. Twice that would be 2(X-6). So Y = 2(X-6). We also know that X + Y = 18 so we have 2 equations:

Y = 2(X-6)

X+Y = 18

Let's take the second equation and solve for Y in terms of X

Y = 18 - X

Now take that result and substitute that back into the first equation that starts with Y, because now you know that Y is also equal to 18 - X, now you have:

18 - X = 2(X - 6)

Let's solve for X

18 - X = 2X - 12

18 - 3X = - 12

- 3X = - 30

X = 10 <--number of home runs Alice Hit

That leaves us with Y = 8 <---number of home runs Peter hit

Go back to the original question and make sure the answer fits. The difference between 10 and 6 is 4 and twice that is 8, the number Peter hit. 10 + 8 = 18. Good to go!