SOLUTION: Dan 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 5 clients who di

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Dan 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 5 clients who di      Log On


   

Question 1158544: Dan 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 5 clients who did Plan A and 3 who did plan B. On Saturday there were 2 clients who did Plan A and 12 who did Plan B. Dan trained his Friday clients for a total of 7 hours and his Saturday clients for a total of 19 hours. How long does each of the workout plans last?
Length of each Plan A workout ___ hour(s) ?
Length of each Plan B workout ___ hour(s) ?
Found 2 solutions by Amily_2190, josgarithmetic:
Answer by Amily_2190(27) About Me  (Show Source):
You can put this solution on YOUR website!
Lets say
Plan A= A
Plan B= B
Friday: 5 Plan A and 3 Plan B for a total of 7 hours 5A%2B3B=7
Saturday: 2 Plan A and 12 Plan B for a total of 12 hrs 2A%2B12B=12
Now we solve for each variable using elimination:
-Multiply the first equation by negative 4 to cancel out the positive 12 B in the second equation.
-4(5A+3B)=-4(7)
-20A-12B=-28

-20A-12B=-28
2A+12B=12
(Add equations)
-18A=-16
A=-16/-18= 8%2F9
Now we solve for B by substituting the value of A into one equation
2A+12B=12
2(8/9)+12B=12
(16/9)+12B=12
12B=92/9
B=23%2F27

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
PLANS    FRID     SAT

       qty rate   qty  rate
 
A       5   a      2   a


B      3   b      12   b


TOTALS    7       19

a, hours per client plan A
b, hours per client plan B

system%285a%2B3b=7%2C2a%2B12b=19%29