Elementary System of Equations Word Problem

Question

We are trying to help our daughter with her math homework and can't seem to find how to do this.

K, E and S volunteer at the hospital. In a week, K volunteers 3 hours more than E does and S volunteers 1 hour less than E. Over 3 weeks, the number of hours K volunteers is equal to the sum of E's and S's volunteer hours in 3 weeks. Complete the table to find out how many hours each person volunteers each weeks.

K - how many volunteer hours per weeK? How many in 3 weeks? E - how many volunteer hours per weeK? How many in 3 weeks? S - how many volunteer hours per weeK? How many in 3 weeks?

Answer 1

We're assuming that each person volunteers the same number of hours every week, so the second datum might just as well say that in one week K volunteers the sum of the number of hours that E and S do. So, putting this together with the first datum, since K volunteers 3 more hours than E, we conclude that S volunteers 3 hours a week. Can you take it from here?

Answer 2

You can set up a couple equations, then solve $$(1) K=E+3$$ $$(2)S=E-1$$ $$(3)3K=3E+3S$$

Substitute (1) and (2) into (3), where you get $$3E+9=3E+3E-3$$ Simplify, then you get $$E=4$$ Plug this into equations (1) and (2), where you get $K=7$ and $S=3$

Answer:

K in 1 week=7; K in 3 weeks=21

E in 1 week=4; E in 3 weeks=12

S in 1 week=3; S in 3 weeks=9