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Question 1104624: I NEED HELP WITH THIS QUESTION, PLEASE HELP ME FIND THE FULL ANSWER!
Linda 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 Monday there were
3
clients who did Plan A and
2
who did Plan B. On Tuesday there were
8
clients who did Plan A and
4
who did Plan B. Linda trained her Monday clients for a total of
4
hours and her Tuesday clients for a total of
9
hours. How long does each of the workout plans last?
LENGTH OF EACH PLAN A WORK OUT:
LENGTH OF EACH PLAN B WORK OUT:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the number of hours for each plan A workout.
let y equal the number of hours for each plan B workout.
on monday, there were 3 clients who did plan A workout and 2 clients who did plan B workout for a total of 4 hours.
the formula for monday becomes 3x + 2y = 4
on tuesday, there were 8 clients who did plan A workout and 4 clients who did plan B workout for a total of 9 hours.
the formula for tuesday becomes 8x + 4y = 9
you have to solve these 2 equations simultaneously.
they are:
3x + 2y = 4
8x + 4y = 9
multiply both sides of the first equation by 2 and leave the second equation as is to get:
6x + 4y = 8
8x + 4y = 9
subtract the first equation from the second to get 2x = 1
solve for x to get x = .5
go back to the first original equation of 3x + 2y = 4 and solve for y to get y = 1.25
go back to the second original equation of 8x + 4y = 9 and replace x with .5 and y with 1.25 to get 8 * .5 + 4 * 1.25 = 9
simplify it to get 4 + 5 = 9 which is true.
this confirms the solution is correct.
the solution is:
the length of a plan A workout is .5 hours.
the length of a plan B workout is 1.25 hours.
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