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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.

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yeraldincallejas05

Answer:

Y=8

Step-by-step 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!

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