Question

Ruth is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 5 male costumes, which used 52 yards of fabric. Today, she sewed 5 female costumes and 2 male costumes, which used a total of 76 yards. How many yards of fabric does each type of costume require? yards of fabric, and every male costume requires Each female costume requires yards.

Answer 1

Each female costume requires 12 yards of fabric, and each male costume requires 8 yards of fabric.

Step-by-step explanation:

In this problem, we are given the amount of fabric used to make costumes for the local children's theater company. We are also given the number of female and male costumes sewn each day. We need to find out how many yards of fabric each type of costume requires.

Let's start by assigning variables to the unknowns. Let x represent the number of yards of fabric required for each female costume, and let y represent the number of yards of fabric required for each male costume.

Based on the information given, we can set up two equations:

1. 1x + 5y = 52 (equation representing the fabric used yesterday)
2. 5x + 2y = 76 (equation representing the fabric used today)

We can solve this system of equations using the substitution method or the elimination method. Let's use the elimination method:

1. Multiply equation 1 by 5, and equation 2 by 1 to make the coefficients of y the same:

5(1x + 5y) = 5(52)

1(5x + 2y) = 1(76)

1. Simplify the equations:

5x + 25y = 260

5x + 2y = 76

1. Subtract equation 2 from equation 1 to eliminate x:

(5x + 25y) - (5x + 2y) = 260 - 76

1. Simplify the equation:

23y = 184

1. Divide both sides of the equation by 23 to solve for y:

y = 8

1. Substitute the value of y into one of the original equations to solve for x:

5x + 2(8) = 76

1. Simplify the equation:

5x + 16 = 76

1. Subtract 16 from both sides of the equation:

5x = 60

1. Divide both sides of the equation by 5 to solve for x:

x = 12

Therefore, each female costume requires 12 yards of fabric, and each male costume requires 8 yards of fabric.

Answer 2

Given:

Yesterday:

1 female and 5 male = 52 yards

Today:

5 female and 2 male = 76 yards

Let's find the number of yards of fabric each type of costume requires.

Let F represent the number if yards for each female customer use.

Let M represent the number of yards each male customer uses.

From this situation, we have the system of equations:

1F + 5M = 52

5F + 2M = 76

Now, let's solve the system of equations simultaneously using substitution method.

Rewrite equation 1 for F:

F = 52 - 5M

Substitute 52 - 5M for F in equation 2:

`\begin{gathered} 5F+2M=76 \\ \\ 5(52-5M)+2M=76 \\ \\ 5(52)+5(-5M)+2M=76 \\ \\ 260-25M+2M=76 \\ \\ 260-23M=76 \end{gathered}`

Subtract 260 from both sides:

`\begin{gathered} 260-260-23M=76-260 \\ \\ -23M=-184 \end{gathered}`

Divide both sides by -23:

`\begin{gathered} (-23M)/(-23)=(-184)/(-23) \\ \\ M=8 \end{gathered}`

Substitute 8 for M in either of the equations:

F = 52 - 5M

F = 52 - 5(8)

F = 52 - 40

F = 12

Therefore, we have the solution:

F = 12, M = 8

Each male customer requires 8 yards while each female customer requires 12 yards.

ANSWER:

• Male customer = 8 yards

,

• Female customer = 12 yards