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Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.9 hours, and Kara can build one in 1.2 hours. One week, Mei builds twice as many computers, and the two spend a total of 24 hours on their project. During a typical week, Mei and Kara spend 15 hours building computers. How many computers do they each make during a typical week?

Answer :

Final answer:

During a typical week, Mei builds 10 computers and Kara builds 5 computers. We use a system of equations based on their building rates and weekly work hours to calculate the number of computers built.

Explanation:

Calculating Computers Built per Week by Mei and Kara

To find out how many computers Mei and Kara make during a typical week, we first need to establish a system of equations based on the given information.

Mei can build a computer in 0.9 hours, and Kara can build one in 1.2 hours.

Let M represent the number of computers Mei builds in a week

K be the number of computers Kara builds in the same period

Given that Mei builds twice as many as Kara, we can write that as M = 2K.

One week, they spent a total of 24 hours building computers.

This can be represented as the equation 0.9M + 1.2K = 24.

Substituting M from the first equation into the second equation,

we get 0.9(2K) + 1.2K = 24, which simplifies to

3K = 24, solving for K, we get K = 8.

Therefore, M = 2K = 2 × 8 = 16.

In a typical week where they spend 15 hours building computers, we use the same approach.

We have 0.9M + 1.2K = 15. Substituting M into this equation from M = 2K, we get

0.9(2K) + 1.2K = 15,

simplifying to 3K = 15 and solving for K, we find K = 5.

Thus, Mei builds 10 computers (M = 2 × 5).

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