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Question 1208364: Alan 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 Monday there were 2 clients who did Plan A and 5 who did Plan B. On Tuesday there were 8 clients who did Plan A and 3 who did Plan B. Alan trained his Monday clients for a total of 8 hours and his Tuesday clients for a total of 15 hours. How long does each of the workout plans last?
Answer by ikleyn(52858)   (Show Source):
You can put this solution on YOUR website! .
Alan 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 Monday there were 2 clients who did Plan A and 5 who did Plan B.
On Tuesday there were 8 clients who did Plan A and 3 who did Plan B.
Alan trained his Monday clients for a total of 8 hours and his Tuesday clients for a total of 15 hours.
How long does each of the workout plans last?
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Let "a" be the hours for plan A;
"b" be the hours for plan B.
As you read the problem, write two equations
2a + 5b = 8 (1) (Monday hours)
8a + 3b = 15 (2) Tuesday hours)
So, you have this system of two equations in two unknown.
To find "a" and "b", solve it using the Elimination method.
For it, multiply equation (1) by 4; kepp equation (2) as is.
New system is
8a + 20b = 32, (1')
8a + 3b = 15. (2')
From eq.(2') subtract eq.(1'). You will get
20b - 3b = 32 - 15
17b = 17
b = 17/17 = 1.
So, plan B is 1 hour.
To find "a" substitute b= 1 into equation (1)
2a + 5*1 = 8
2a = 8 - 5 = 3
a = 3/2 = 1.5.
ANSWER. Plan A is 1.5 hours. Plan B is 1 hour.
Solved.
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