Question 1208364
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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.


<U>ANSWER</U>.  Plan A is 1.5 hours.  Plan B is 1 hour.
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Solved.