Elliot collects miniature toy cars. He wants to fill 4 display cases. Each display case holds 15 cars. He has 28 cars now, and he is able to buy 3 more every month with the money he saves from his allowance. How many more months will it be until Elliot has enough cars to fill all 4 display cases?

Question

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Elliot will have enough cars to fill 4 display cases in
months.

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Answer 1

First, let's determine how many cars Elliot needs to fill all 4 display cases.

Each display case holds 15 cars, so for 4 display cases, he needs:

\[ 4 \text{ cases} \times 15 \text{ cars/case} = 60 \text{ cars} \]

Elliot currently has 28 cars. To find out how many more cars he needs, we subtract the number of cars he has from the total required:

\[ 60 \text{ cars} - 28 \text{ cars} = 32 \text{ cars} \]

Next, we know that Elliot can buy 3 more cars every month. To find out how many months it will take for him to acquire the additional 32 cars, we set up the following equation:

\[ \text{Number of months} = \frac{\text{Number of cars needed}}{\text{Number of cars bought per month}} \]

Substituting in the values we have:

\[ \text{Number of months} = \frac{32 \text{ cars}}{3 \text{ cars/month}} = \frac{32}{3} \approx 10.67 \]

Since he cannot wait a fraction of a month, we round up to the next whole number:

\[ \lceil 10.67 \rceil = 11 \]

Therefore, Elliot will have enough cars to fill 4 display cases in 11 months.