Elizabeth, a costume designer for the Silvergrove City Opera, is making costumes for the chorus members in an upcoming performance. While costuming this group of singers, Elizabeth must keep costs below $1,900. Male costumes cost $13.23 to make and female costumes cost $37.01.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of male costumes
y = the number of female costumes

Answer 1

To write the inequality in standard form that describes the situation, we need to express the total cost of the costumes in terms of the number of male (x) and female (y) costumes.

The total cost for male costumes is $13.23 per costume, so the cost for x male costumes is:

\[ 13.23x \]

The total cost for female costumes is $37.01 per costume, so the cost for y female costumes is:

\[ 37.01y \]

The total cost for both male and female costumes must be less than or equal to $1,900. Thus, we can write the inequality as:

\[ 13.23x + 37.01y \leq 1900 \]

To put this into standard form, we usually want the variables on one side and the constant on the other. The standard form of a linear inequality is: \[ Ax + By \leq C \] Where A, B, and C are constants and A should be non-negative.

In this case, the inequality is already in the correct form:

• The coefficients are:
  • A = 13.23
  • B = 37.01
  • C = 1900

Thus, the final standard form of the inequality is:

\[ 13.23x + 37.01y \leq 1900 \]