Word Problem: Attempted to problem, want to make sure it was set up correctly

Question

The number of apples is twice as much as the number of pears.  If three pears are distributed to each student, there will be 2 pears left over.  If 7 apples are distributed to each student, there will be 6 apples short.  How many apples and how many pears are there?

Answer 1

A = number of apples

P = number of pears

 

Number of students, N, can be written in terms of number of pears:

 

N = (P-2)/3

 

Number of students, N, can also be written in terms of number of apples as:

 

N = (A+6)/7

 

Setting these two equations equal to each other:

 

(P-2)/3 = (A+6)/7

 

Number of apples is twice as much as pears:

 

A = 2P

 

Replacing A from the previous equation with P:

 

(P-2)/3 = (2P+6)/7

7P-14 = 6P + 18

P = 32

A = 2(32) = 64