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The physical education instructor asked each student to do a total of $36$ pull-ups in $1$ minute. The instructor wanted students to do $8$ times as many push-ups as pull-ups. Write a system of equations of linear equations that represents this situation. How many pull-ups and push-ups were required in $1$ minute.

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Write and solve equations for proportional relationships

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Q. The physical education instructor asked each student to do a total of

36

pull-ups in

1

minute. The instructor wanted students to do

8

times as many push-ups as pull-ups. Write a system of equations of linear equations that represents this situation. How many pull-ups and push-ups were required in

1

minute.

Denote pull-ups as $p$ : Let's denote the number of pull-ups as $p$ and the number of push-ups as $s$ . According to the instructor, each student is required to do a total of $36$ pull-ups in $1$ minute. This gives us our first equation: $\newline$ $p = 36$
Calculate push-ups: Next, we are told that the instructor wants students to do $8$ times as many push-ups as pull-ups. This gives us our second equation: $\newline$ $s = 8p$
Substitute $p$ into $s$ : Now we can substitute the value of $p$ from the first equation into the second equation to find the number of push-ups: $\newline$ $s = 8 \times 36$
Perform multiplication: Performing the multiplication gives us the number of push-ups: $s = 288$
Final system of equations: We now have both values that the instructor has asked for: $p$ for pull-ups and $s$ for push-ups. The system of equations is: $\newline$ $p = 36$ $\newline$ $s = 8p$ $\newline$ And substituting $p$ into the second equation, we get: $\newline$ $s = 288$

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