SOLUTION: Susan 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

Algebra ->  Linear-equations -> SOLUTION: Susan 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       Log On


   

Question 1152582: Susan 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 6 clients who did Plan A and 2 who did Plan B. Susan trained her Wednesday clients for a total of 10 hours and her Thursday clients for a total of 10 hours. How long does each of the workout plans last?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of minutes for plan A.
y = number of minutes for plan B.
each day, the trainer worked for 10 hours.
10 * 60 = 600 minutes.
you get two equations that need to be solved simultaneously.
they are:
3x + 5y = 600
6x + 2y = 600
multiply both sides of the first equation by 2 and leave the second equation as is to get:
6x + 10y = 1200
6x + 2y = 600
subtract the second equation from the first to gt:
8y = 600
solve for y to get:
y = 600 / 8 = 75
replace y with 75 in the first original equation to get:
3x + 5y = 600 becomes 3x + 5 * 75 = 600
solve for x to get:
x = (600 - 5 * 75) / 3 = 75
you have:
x = 75 and y = 75
replace x and y in the two original equations to get:
3x + 5y = 600 becomes 3 * 75 + 5 * 75 = 600 which becomes 8 * 75 = 600 which becomes 600 = 600 which is true.
6x + 2y = 600 becomes 6 * 75 + 2 * 75 = 600 which becomes 8 * 75 = 600 which becomes 600 = 600 which is also true.
the values of x and y look good.
your solution is that each plan session last for 75 minutes.