Question

Donna 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 5 clients who did Plan A and 6 who did Plan B. On Thursday there were 3 clients who did Plan A and 2 who did Plan B. Donna trained her Wednesday clients for a total of 12 hours and her Thursday clients for a total of 6 hours. How long does each of the workout plans last?
LengthofeachPlanAworkout:hour(s)

LengthofeachPlanBworkout:hour(s)

Answer 1

X=hours of plan A
y=hours of plan B

wed: 5x+6y=12
thu: 3x+2y=6

so
5x+6y=12 and
3x+2y=6
we can eliminate y's by multiplying 2nd equation by -3 and adding to first equation

-9x-6y=-18
5x+6y=12 +
-4x+0y=-6

-4x=-6
divid both sides by -4
x=-6/-4
x=3/2
x=1.5

sub back

3x+2y=6
3(1.5)+2y=6
4.5+2y=6
2y=1.5
y=0.75



Plan A=1.5 hours
Plan B=0.75 hours