How many home runs did each player hit that season?

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?

Answer 1

Hi Alex

 

Let's start by saying Alice hit X number of home runs.  And Peter hit Y number of home runs.

 

Peter hit twice the difference of the number Alice hit and 6.  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!

 

All the best

 

Lori