Question

yoko the trainer has two solo workout plans that she offers her clients: plan a and plan b. each client does either one or the other (not both). on wednesday there were 3 clients who did plan a and 5 who did plan b. on thursday there were 12 clients who did plan a and 2 who did plan b. yoko trained her wednesday clients for a total of 7 hours and her thursday clients for a total of 19 hours. how long does each of the workout plans last?
length of each plan a workout: hour(s)
length of each plan b workout: hour(s)

Explanation:

Step1: Define variables

Let \( x \) be the length of Plan A workout (in hours) and \( y \) be the length of Plan B workout (in hours).

Step2: Set up equations from Wednesday

On Wednesday, 3 clients did Plan A and 5 did Plan B, total 7 hours. So:
\( 3x + 5y = 7 \)

Step3: Set up equations from Thursday

On Thursday, 12 clients did Plan A and 2 did Plan B, total 19 hours. So:
\( 12x + 2y = 19 \)

Step4: Solve the system of equations

First, simplify the second equation by dividing by 2: \( 6x + y = \frac{19}{2}=9.5 \), so \( y = 9.5 - 6x \)

Substitute \( y = 9.5 - 6x \) into the first equation:
\( 3x + 5(9.5 - 6x) = 7 \)
\( 3x + 47.5 - 30x = 7 \)
\( -27x = 7 - 47.5 \)
\( -27x = -40.5 \)
\( x = \frac{-40.5}{-27} = 1.5 \)

Step5: Find y

Substitute \( x = 1.5 \) into \( y = 9.5 - 6x \):
\( y = 9.5 - 6(1.5) = 9.5 - 9 = 0.5 \)

Answer:

Length of each Plan A workout: \( 1.5 \) hour(s)
Length of each Plan B workout: \( 0.5 \) hour(s)