Question

Volunteers A, B, and C volunteered to stuff 792 envelopes with newsletters for a certain reelection campaign. Volunteer A could assemble 148 envelopes per hour, volunteer B, 114 envelopes per hour, and volunteer C, 139 envelopes per hour. They worked a total of 6 hours. The sum of the number of hours that volunteers B and C spent was twice what volunteer A spent. How long did each of them work?solve by elimination and substition

Answer 1

For the information given in the statement, let be

A = the hours that volunteer A worked

B = the hours that volunteer B worked

C = the hours that volunteer C worked

Then, you have the following system of linear equations

$\begin{cases}148A+114B+139C=792\text{ (1)} \\ A+B+C=6\text{ (2)} \\ B+C=2A\text{ (3)}\end{cases}$

Now, using the elimination method you have

*First multiply equation (2) by -148