Question

18. Bob is 30 pounds heavier than Sara. If Bob and Sara each gain 30 pounds Bob's weight will be 25% greater than Sara's weight. How much does Bob weigh right now? A 90 120 150 180 210

Answer 1

Solution:

Let B = Bob's PRESENT weight
Let S = Sara's PRESENT weight
"Bob is 30 pounds heavier than Sara."
We can write: B = S + 30 (as you have)

Adding 30 to each weight, we get:
Bob's NEW weight = B + 30
Sara's NEW weight = S + 30

ASIDE: If S = Sara's PRESENT weight, then S+30 = her NEW weight.
You said S+60 = Sara's weight, but this represents a weight gain of 60 pounds.

"Bob's weight is 25% greater than Sara's weight."
In other words: (Bob's NEW weight) = 1.25(Sarah's NEW weight)
We can write: B + 30 = 1.25(S + 30)

We now have a system of two equations:
B = S + 30
B + 30 = 1.25(S + 30)

When we solve this system, we get: S = 90 and B = 120

So, Sarah's PRESENT weight is 90 pounds, and Bob's PRESENT weight is 120 pounds

So option B is the correct answer