Question 1187750: Milan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B.
Each client does either one or the other (not both).
On Friday there were 3 clients who did Plan A and 2 who did Plan B.
On Saturday there were 8 clients who did Plan A and 4 who did Plan B.
Milan trained his Friday clients for a total of 7hours and his Saturday clients for a total of 17hours.
How long does each of the workout plans last?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a equal the the number of hours spent on plan A.
let b equal the number of hours spent on plan B.
on friday, there were 3 who did plan A and 2 who did plan B for a total of 7 hours.
on saturday, there were 8 who did plan A and 4 who did plan B for a total of 17 hours.
you have two equations that need to be solved simultaneously.
that means the same value of a and b for both equations.
the requations are:
3a + 2b = 7
8a + 4b = 17
multiply both sides of the first equAtion by 2 and leave the second equation as is to get:
6a + 4b = 14
8a + 4b = 17
subtract the first equation from the second to get:
2a = 3
solve for a to get:
a = 3/2
replace a with 3/2 in either equation to get:
6a + 4b = 14 becomes 6 * 3/2 + 4b = 14 which becomes 9 + 4b = 14
8a + 4b = 17 becomes 8 * 3/2 + 4b = 17 which becomes 12 + 4b = 17
solve for b in both equations to get:
4b = 14 - 9 which becomes 4b = 5 which becomes b = 5/4.
4b = 17 - 12 which becomes 4b = 5 which becomes b = 5/4.
you have:
a = 3/2 and b = 5/4.
replace a and b in your original equaiton to see if they are true.
3a + 2b = 7 becomes 3 * 3/2 + 2 * 5/4 = 7 which becomes 9/2 + 10/4 = 7 which becomes 18/4 + 10/4 = 7 which becomes 28/4 = 7 which becomes 7 = 7, confirming the values of a and b are good for the first equation.
8a + 4b = 17 becomes 8 * 3/2 + 4 * 5/4 = 17 which becomes 24/2 + 20/4 = 17 which becomes 48/4 + 20/4 = 17 which becomes 68/4 = 17 which becomes 17 = 17, confirming the value of a and b are good for the second equation.
your solution is that plan A workout lasts 1.5 hours and plan B workout lasts 1.25 hours.
let me know if you have any questions.
theo
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