Systems of linear equations and problem solving

Question

in 2012, the average emails sent or recieved 115- emails each day. The number of emails recieved was 1 more than twice the number sent. how many were sent and how many were recieved each day

Answer 1

First assign variables to the things you want to figure out (the "unknowns")

 

Let r be the number of emails received, and let s be the number sent.

 

So we know two things from the statements that were made:

 

s + r = 115

r = 2s + 1

 

That's two equations with two unknowns, so they can be solved.

 

Since one of the equations is an explicit expression for one of the unknowns in terms of the other, the easiest approach is probably substitution:

 

s + r = 115

s + (2s + 1) = 115

3s + 1 = 115

3s = 114

s = 38

 

r = 2s + 1 = 2*38 + 1 = 76 + 1 = 77

 

So the number sent was 38 and the number received was 77.