Question

m. the physical education instructor asked each student to do a total of 36 pull - ups and push - ups. the instructor wanted students to do 8 times as many push - ups as pull - ups. write a system of linear equations where x represents the number of pull - ups and y represents the number of push - ups required in 1 minute. solve the system by substitution.

Explanation:

Step1: Define variables and set up equations

Let \( x \) be the number of pull - ups and \( y \) be the number of push - ups. We know two things:

1. The total number of pull - ups and push - ups is 36, so \( x + y=36 \).
2. The number of push - ups is 8 times the number of pull - ups, so \( y = 8x \).

Step2: Substitute \( y = 8x \) into \( x + y=36 \)

Substitute \( y\) in the first equation with \( 8x \) from the second equation. We get \( x+8x = 36 \).
Combine like terms: \( 9x=36 \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 9x = 36 \) by 9: \( x=\frac{36}{9}=4 \).

Step4: Solve for \( y \)

Substitute \( x = 4 \) into the equation \( y = 8x \). Then \( y=8\times4 = 32 \).

Answer:

The number of pull - ups \( x = 4 \) and the number of push - ups \( y = 32 \).