Question

Abe and Ben each have a certain number of dollars. If Abe gives Ben $5 then Abe and Ben will have the same number of dollars. If Ben gives Abe $5 then Abe will have twice as many dollars as Ben. Let A=Abe's original dollars B= Bens original dollars. Express the problem as a linear system in A and B. Solve the system for A and B by addition or substitution. Tell who had what and use dollar sign $.

Answer 1

A = 5 + B
A + 5 = 2B

Let's get one of the variables on one side.

A = 5 + B
A = 2B - 5

By the transitive property

5 + B = 2B - 5

Solve for B.

5 = B - 5
10 = B

Use 10 = B in an earlier equation to find A.

A = 5 + B
A = 5 + 10
A = 15

Abe has 15$ and Ben has 10$.