Alan, Bob, and Charles worked together on a job and earned a combined total of $380. Alan earned $40 less than Bob. Charles earned twice as much as Alan.

Question

How much did Alan earn?

 

 

Answer 1

Let Alan's earnings be a, Bob's earnings be b and that of Charles be c. 

Given that a+b+c=380.  Also given that Alan earned 40 less than Bob.  That translates to a=b-40.  Charles earned twice as much as Alan.  That is, c=2a.  Substitute a=b-40 into c=2a to get c=2(b-40)=2b-80.

 

Substitute a=b-40 and c=2b-80 into a+b+c=380 to get 

b-40+b+2b-80=380.

Combining like terms, we get 4b-120=380.  Adding 120 to both sides of the equation, we get, 4b=500 and dividing by 4 on both sides, we get b=125.

 

Since we want to know what Alan earned, substitute b=125 back into a=b-40=125-40=85

 

Therefore, Alan earned $85!