I need help on this

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

There are two equations to be solved here.  The first one we assign variables to the home runs Peter hits, P, and Alice hits, A.

 

P=2*(A-6)

 

The second equation is the sum of both players home runs.

P + A = 18

Solving for P yields

P=18-A

 

We substitute the solution for P into the first equation and solve for A.

(18-A) = 2*(A-6)

18 - A = 2A - 12

3A = 30

A = 10

 

Now that A is known, we can plug it into either equations for P to find how many home runs Peter hits

P=18 - (10) = 8

or

P=2((10)-4) = 8

 

Final Answers: Peter hits 8 home runs and Alice hits 10 home runs