Question
Tristan, a costume designer for the Livingston City Opera, is making costumes for the chorus members in an upcoming performance. While costuming this group of singers, Tristan must keep costs below $1,500. Male costumes cost $13 to make and female costumes cost $23. 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
Answers
GPT-4o mini
To define the situation with an inequality, we can start with the expressions for the cost of the male and female costumes.
The cost for male costumes is represented as \(13x\) (since each male costume costs $13) and the cost for female costumes is represented as \(23y\) (since each female costume costs $23).
Tristan wants to keep the total cost below $1,500, which can be expressed with the inequality:
\[
13x + 23y < 1500
\]
To write this in standard form, we can rewrite it as follows:
\[
13x + 23y - 1500 < 0
\]
If you prefer the inequality in standard polynomial form (as \(Ax + By + C \leq 0\) or \(Ax + By + C \geq 0\)), it could also be rearranged as:
\[
13x + 23y - 1500 \leq 0
\]
Thus, the inequality that describes the situation is:
\[
13x + 23y \leq 1500
\]
This inequality states that the total cost of costumes must be less than or equal to $1,500.
The cost for male costumes is represented as \(13x\) (since each male costume costs $13) and the cost for female costumes is represented as \(23y\) (since each female costume costs $23).
Tristan wants to keep the total cost below $1,500, which can be expressed with the inequality:
\[
13x + 23y < 1500
\]
To write this in standard form, we can rewrite it as follows:
\[
13x + 23y - 1500 < 0
\]
If you prefer the inequality in standard polynomial form (as \(Ax + By + C \leq 0\) or \(Ax + By + C \geq 0\)), it could also be rearranged as:
\[
13x + 23y - 1500 \leq 0
\]
Thus, the inequality that describes the situation is:
\[
13x + 23y \leq 1500
\]
This inequality states that the total cost of costumes must be less than or equal to $1,500.