Question

Judy is a costume designer for the local children's theater company. Yesterday, she sewed 2 female costumes and 2 male costumes, which used 46 meters of fabric. Today, she sewed 5 female costumes and 1 male costume, which used a total of 79 meters. How many meters of fabric does each type of costume require?

a. Female costumes: 8 meters, Male costumes: 10 meters
b. Female costumes: 10 meters, Male costumes: 9 meters
c. Female costumes: 9 meters, Male costumes: 8 meters
d. Female costumes: 12 meters, Male costumes: 7 meters

Answer 1

Female costumes require 14 meters of fabric, and male costumes require 9 meters of fabric.

How to determine the amount of fabric required

To determine the amount of fabric required for each type of costume, let's assign variables.

Let F represent the number of meters of fabric required for a female costume, and let M represent the number of meters of fabric required for a male costume.

From the given information, set up the following equations:

Yesterday:

2F + 2M = 46 meters --(Equation 1)

Today:

5F + 1M = 79 meters --(Equation 2)

To solve this system of equations, use various methods, such as substitution or elimination.

Let's use the elimination method.

Multiply Equation 1 by 5 and Equation 2 by 2 to eliminate M:

10F + 10M = 230 meters --(Equation 3)

10F + 2M = 158 meters --(Equation 4)

Subtract Equation 4 from Equation 3:

8M = 72 meters

M = 72/8

M = 9 meters

Substitute the value of M into Equation 1:

2F + 2(9) = 46 meters

2F + 18 = 46 meters

2F = 46 - 18

2F = 28 meters

F = 28/2

F = 14 meters

Therefore, the solution is:

Female costumes require 14 meters of fabric, and male costumes require 9 meters of fabric.