Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Kylie is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 4 male costumes, which used 24 meters of fabric. Today, she sewed 4 female costumes and 4 male costumes, which used a total of 60 meters. How many meters of fabric does each type of costume require?Each female costume requires meters of fabric, and every male costume requires meters.
Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Kylie is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 4 male costumes, which used 24 meters of fabric. Today, she sewed 4 female costumes and 4 male costumes, which used a total of 60 meters. How many meters of fabric does each type of costume require?Each female costume requires meters of fabric, and every male costume requires meters.
Solution
Let's denote the amount of fabric required for a female costume as F and for a male costume as M.
From the problem, we can write two equations:
1F + 4M = 24 (This is from the first day when Kylie sewed 1 female costume and 4 male costumes which used 24 meters of fabric)
4F + 4M = 60 (This is from the second day when Kylie sewed 4 female costumes and 4 male costumes which used 60 meters of fabric)
Now, we can solve this system of equations using the elimination method.
First, let's subtract the first equation from the second to eliminate M:
4F + 4M - (1F + 4M) = 60 - 24 3F = 36 F = 36 / 3 F = 12
So, each female costume requires 12 meters of fabric.
Now, let's substitute F = 12 into the first equation to find M:
1*12 + 4M = 24 12 + 4M = 24 4M = 24 - 12 4M = 12 M = 12 / 4 M = 3
So, each male costume requires 3 meters of fabric.
Therefore, each female costume requires 12 meters of fabric, and every male costume requires 3 meters.
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