Question

Aaron and Carl are working to earn money for prom. Aaron has $40 and is earning $6 a month for prom. Carl has $64 and $4 a week. How many weeks till they have the same amount?

Answer 1

After 10 weeks, Aaron and Carl will have approximately the same amount of money saved for prom. Because Carl is paid weekly, we convert his earnings to monthly for comparison, and then back to weekly to find the time until their savings are equal.

Step-by-step explanation:

To find out when Aaron and Carl will have the same amount of money for prom, we set up an equation where Aaron starts with $40 and earns $6 per month, while Carl starts with $64 and earns $4 per week. Since we know there are about 4 weeks in a month, we can convert Carl's weekly earnings to monthly by multiplying by 4.

Aaron's savings: $40 + $6 × months

Carl's savings: $64 + $4 × (weeks) = $64 + $4 × (4 × months) = $64 + $16 × months

Now we equate the two expressions for their savings:

$40 + $6 × months = $64 + $16 × months

Solving for months gives us:

$10 × months = $24

months = $24 / $10

months = 2.4

Since Carl earns money weekly, we then convert the 2.4 months into weeks:

weeks = 2.4 × 4

weeks = 9.6

Given that partial weeks are not practical in this context, we can deduce that after 10 weeks, Aaron and Carl will have approximately the same amount of money saved for prom.