Question

In one baseball season, Peter hit twice the difference of the number of home runs Alice hit and 9. Altogether, they hit 27 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

Answer: Down below

(I know its late but it helps others)

Explanation:Write a verbal description of the basic situation.

The total number of home runs is 27.

Since, h represents Alice's home runs, 2(h − 9) represents Peter's home runs.

Therefore, h + 2(h − 9) = 27. Solve the equation for h.

h + 2(h − 9) = 27

h + 2h − 18 = 27 Distributive Property

3h − 18 = 27 Combine like terms.

3h − 18 + 18 = 27 + 18 Addition Property of Equality

3h = 45

3h

3

 =  

45

3

 Division Property of Equality

h = 15

So, Alice hit 15 home runs and Peter hit 2(15 − 9) = 12 home runs.

Answer 2

Let h = the no. of home runs for Alice 
Let 2(h-9) = for Peter's home run


Alice number of home run is 15, below is the solution:

45 = 3h
45/3 = 3h/3 
15 = h 



And for Peter, the number of home run is 12, below is the solution:

 = 2(h - 9) 
= 2 (15 - 9) ⇒15 is the number of Alice's home run 
= 2 (6)
= 12


I hope it helps.