Question

A school wants to put on a dance recital Middle School dancers have short programs that run 4 minutes long High School performers will dance longer with longer programs 7 Minutes in length the entire program cannot have more than 10 dances in the entire recital must be over in less than 90 minutes what pair of inequalities best represents the number of short middle school dances M and the number of longer high school dances H that can be performed given these limitations

Answer 1

Answer:  The answer is $\textup{M}+\textup{H}\leq 10~~\textup{and}4\textup{M}+7\textup{H}\leq 90.$

Step-by-step explanation: Given that a school wants to put on a dance recital. The programs of Middle school dancer will be short of 4 minutes each and programmes of High school performers will be long of 7 minutes each.

Number of middle school dances is "M" and number od high school dances is "H".

Since there cannot be more than 10 dances all together, so fisrt inequality can be written as

$\textup{M}+\textup{H}\leq 10.$

Also, the entire recital must take maximum 90 minutes, so the second inequality can be written as

$4\textup{M}+7\textup{H}\leq 90.$

Thus, the pair of inequalities is

$\textup{M}+\textup{H}\leq 10,\\\\4\textup{M}+7\textup{H}\leq 90.$