Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Kiera is a costume designer for the local children's theater company. Yesterday, she sewed 4 female costumes and 3 male costumes, which used 52 yards of fabric. Today, she sewed 5 female costumes and 3 male costumes, which used a total of 62 yards. How many yards of fabric does each type of costume require?

Answer 1

the female costume requires 10 yards of fabric and the male costume requires 4 yards of fabric

Step-by-step explanation:

let the female costumes = x

let the male costumes = y

she sewed 4 female costumes and 3 male costumes = 4x + 3y

Total yards of fabric used = 52

The system of equation that describes this:

4x + 3y = 52

she sewed 5 female costumes and 3 male costumes = 5x + 3y

Total yards of fabric used = 62

The system of equation that describes this:

5x + 3y = 62

To find out number of yards for eachfabric, we would solve the equations:

4x + 3y = 52 ...equation 1

5x + 3y = 62 ...equation 2

using elimination method:

we would subtract equation 1 from 2 to eliminate y (it has same coefficient in both equations)

5x - 4x + 3y - 3y = 62 - 52

x + 0 = 10

x = 10

substitute for x in any of the equation:

using equation 1: 4x + 3y = 52

4(10) + 3y = 52

40 + 3y = 52

3y = 52 - 40

3y = 12

3y/3 = 12/3

y = 4

Hence, the female costume requires 10 yards of fabric and the male costume requires 4 yards of fabric