Question

Jack and Sara are both saving money from their allowance. They both began saving at the same time. Jack started with $65.00 and adds $5.50 to his savings every month. Sara did not have a starting amount but adds $8.75 to her savings every month. Which equation could be used to determine how many months, m, it will take before Jack and Sara both have saved the same amount of money?

a) 65 + 5.50m = 8.75m
b) 65 + 5.50m = 65 + 8.75m
c) 5.50m = 8.75m
d) 65 + 8.75m = 5.50m

Answer 1

The correct equation to determine when Jack and Sara will have the same amount saved is 65 + 5.50m = 8.75m. This equation sets Jack's starting savings plus his monthly contributions equal to Sara's monthly contributions, accounting for the differences in their savings rates.

Step-by-step explanation:

The question is asking for an equation that could be used to determine the number of months, m, it would take for Jack and Sara to have the same amount of savings from their allowance. Jack started with $65.00 and adds $5.50 every month to his savings, while Sara started with $0.00 and adds $8.75 each month. To find when their savings are equal, you set Jack's savings equal to Sara's savings:

Jack's savings: 65 + 5.50m
Sara's savings: 8.75m

Therefore, the correct equation to determine when they will have saved the same amount is:

65 + 5.50m = 8.75m.

This indicates that every month, the difference in their savings decreases by the difference in their monthly savings rates, which is $3.25 ($8.75 - $5.50). When this product equals Jack's initial $65 advantage, they will have the same amount saved.