Alice and Bob's Bicycle Savings

Alice and Bob are each saving for a new bicycle. Alice saves $5 every week while Bob saves $7 each week. If Alice has already saved $20 and Bob has saved $35, how many weeks will it take for Alice to have saved the same amount as Bob?

Let $A$ be Alice’s total savings after $w$ weeks, and let $B$ be Bob’s total savings after $w$ weeks. The equations for their savings can be modeled as:

$A = 20 + 5w$

$B = 35 + 7w$

Set $A = B$ to find the number of weeks $w$.