Question

ms. gupta is planning a dance recital for her students. the maximum duration for the recital is 78 minutes. group dance numbers last 7 minutes and a solo performance lasts 3 minutes. write the inequality in standard form that describes this situation. use the given numbers and the following variables. x = the number of group dances on the program y = the number of solo numbers on the program

Explanation:

Step1: Calculate total time for group dances

The total time for group dances is the time per group - dance times the number of group - dances. Since each group dance lasts 7 minutes and there are \(x\) group dances, the total time for group dances is \(7x\) minutes.

Step2: Calculate total time for solo performances

The total time for solo performances is the time per solo - performance times the number of solo - performances. Since each solo performance lasts 3 minutes and there are \(y\) solo performances, the total time for solo performances is \(3y\) minutes.

Step3: Set up the inequality

The maximum duration of the recital is 78 minutes. So the sum of the time for group dances and solo performances must be less than or equal to 78 minutes. The inequality is \(7x + 3y\leq78\).

Answer:

\(7x + 3y\leq78\)