Joe 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 3 who did plan
b. on tuesday there were 4 clients who did plan a and 8 who did plan
b. joe trained his monday clients for a total of 7 hours and his tuesday clients for a total of 17 hours. how long does each of the workout plans last?

Let workout Plan A last a hours, and Plan B last b hours.

we are assuming personal training for each client.

i)
"On Monday there were 2 clients who did Plan A and 3 who did Plan"

the total time spent is : 2*a + 3*b =2a+3b

ii)
"On Tuesday there were 4 clients who did Plan A and 8 who did Plan B"

the total time spent was 4*a+8*b=4a+8b

iii) "Joe trained his Monday clients for a total of 7 hours"

so 2a+3b = 7

iv)

"Joe trained his Tuesday clients for a total of 17 hours"

so 4a+8b=17

v) thus we have the following system of equations:

2a+3b = 7
4a+8b=17

multiply the first equation by -2, and then add both equations, to eliminate a:

-4a-6b=-14
4a+8b=17

2b=3, so b=3/2

2a+3b = 7
2a+3(3/2)=7
2a+9/2=7
multiply by 2:
4a+9=14
4a=5
a=5/4

Answer :

Plan A lasts 5/4=1.25 h
Plan B lasts 3/2=1.5 h

Where are the following equations?