SOLUTION: Hi! I'm not really sure I understand this problem and I'm having problems formulating a solution. There's an attempt below which should be correct but I think my method is ambig

Algebra ->  Expressions-with-variables -> SOLUTION: Hi! I'm not really sure I understand this problem and I'm having problems formulating a solution. There's an attempt below which should be correct but I think my method is ambig      Log On


   

Question 530315: Hi!
I'm not really sure I understand this problem and I'm having problems formulating a solution. There's an attempt below which should be correct but I think my method is ambiguous. A better method would be appreciated and any other help too!
Paul worked 7 more problems than Jean. Together they worked 55 problems. How many did each boy work?
%287+%2B+Jean%29+%2B+Jean+=+55
7+%2B+2Jean+=+55
2Jean+=+55+-+7
2Jean+=+48
Jean+=+24
Paul worked 7 more than Jean therefore +24+%2B+7+=+31+ problems for Paul
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I can see only one additional step that you might have included!
Let P = The number of problems Paul worked on.
Let J = The number of problems Jean worked on.
1) P = J+7 "Paul worked 7 more problems than Jean."
2) P+J = 55 "Together they worked 55 problems."
Substitute the P from equation 1) for the P in equation 2).
2a) (J+7)+J = 55 Simplify.
2b) 2J+7 = 55 Subtract 7 from both sides.
2c) 2J = 48 Divide by 2.
2d) J = 24 Substitute into equation 1)
1a) P = 24+7
1b) P = 31
Paul worked 31 problems and Jean worked 24 problems.