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Isabelle is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under $\$570$ . A band can play for part of the time at an hourly rate of $\$160$ , and a DJ can play for the remaining time at an hourly rate of $\$75$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of hours the band will play $\newline$ $y =$ the number of hours the DJ will play $\newline$ Choices: $\newline$ (A) $160x + 75y < 570$ $\newline$ (B) $75x + 160y < 570$ $\newline$ (C) $75x + 160y \leq 570$ $\newline$ (D) $160x + 75y \leq 570$

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Write two-variable inequalities: word problems

Full solution

Q. Isabelle is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under

\$570

. A band can play for part of the time at an hourly rate of

\$160

, and a DJ can play for the remaining time at an hourly rate of

\$75

.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours the band will play

\newline

y =

the number of hours the DJ will play

\newline

Choices:

\newline

(A)

160x + 75y < 570

\newline

(B)

75x + 160y < 570

\newline

(C)

75x + 160y \leq 570

\newline

(D)

160x + 75y \leq 570

Calculate Band Cost: Determine the cost for the band. The band charges $\$160$ per hour and the number of hours the band will play is represented by $x$ . Therefore, the total cost for the band is calculated by multiplying the band's charge per hour by the number of hours the band will play, which gives us $160x$ .
Calculate DJ Cost: Determine the cost for the DJ. The DJ charges $\$75$ per hour and the number of hours the DJ will play is represented by $y$ . Therefore, the total cost for the DJ is calculated by multiplying the DJ's charge per hour by the number of hours the DJ will play, which gives us $75y$ .
Combine Total Entertainment Cost: Combine the costs for the band and the DJ to find the total cost of entertainment. The total cost is the sum of the cost for the band and the cost for the DJ, which is $160x + 75y$ .
Set Total Cost Inequality: Isabelle wants to keep the total cost under $\$570$ . Therefore, the inequality that represents this situation is that the total cost for the band and the DJ must be less than $\$570$ . The inequality in standard form is $160x + 75y < 570$ .

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