Algrebra for college students

Question

eric the trainer has two solo workout plans that he offer his clients: plan a and plan b. each client does not with one or the other (not both). on monday there were 3 clients who did plan a and 8 who did plan b. on tuesday there were 5 clients who did plan a and 2 who did plan b. eric trained his monday clients for a total of 15 hours and his tuesday clients for a total of 8 hours. how long does each of the workout plans last?

Answer 1

We can write an equation for Monday (call it M) and one for Tuesday (call it T). With A and B meaning the obvious thing:

(M). 3A + 8B = 15

(T). 5A + 2B = 8

So we have two simultaneous linear equations in two unknowns. We could solve for A and B is several ways, but basically we want to express one variable in terms of the other to give us a linear equation in one unknown. One way is to multiply equation T by 4 and subtract eq. M from it:

20A + 8B = 32

-(3A + 8B) = 15

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17A = 17

This eliminates B, and it's clear that A = 1. Now we can substitute that value for A in either equation and solve for B. Using eq. T:

5*1 + 2B = 8

2B = 3

So B = 3/2. To check, substitute the values we found into eqs. M and T.

M: 3 + 8(3/2) = 15

T: 5 + 2(3/2) = 8

Both equations are valid, so our answer is correct.

Answer 2

Assume plan a lasts x hour, and plan b lasts y hour, then

3x+8y=15

5x+2y=8

solve the system of equations, you get x=1,y=1.5.

plan a lasts 1 hour and plan b lasts 1.5 hours