Question

1. vince is trying to incorporate more exercise into his busy schedule. he has several short exercise routines he can complete at home. last week, he worked out for a total of 22 minutes by doing 1 arm routine and 1 abdominal routine. this week, he has completed 3 arm routines and 2 abdominal routines and spent a total of 56 minutes exercising. how long does each routine last?

a write the two equations for the system & use substitution to solve the system.
equation 1:
equation 2:
b. what does the solution represent?

Explanation:

Step1: Define variables

Let $x$ = time (minutes) of 1 arm routine, $y$ = time (minutes) of 1 abdominal routine.

Step2: Set up first equation

From last week's workout: $x + y = 22$

Step3: Set up second equation

From this week's workout: $3x + 2y = 56$

Step4: Isolate $y$ from Equation1

$y = 22 - x$

Step5: Substitute $y$ into Equation2

$3x + 2(22 - x) = 56$

Step6: Solve for $x$

$3x + 44 - 2x = 56$
$x + 44 = 56$
$x = 56 - 44 = 12$

Step7: Solve for $y$

$y = 22 - 12 = 10$

Answer:

A.
Equation 1: $x + y = 22$
Equation 2: $3x + 2y = 56$
The solved values: Each arm routine lasts 12 minutes, each abdominal routine lasts 10 minutes.

B.
The solution represents the length (in minutes) of each individual exercise routine: 12 minutes for one arm routine, and 10 minutes for one abdominal routine.