SOLUTION: If Albert gives Bob 10 cents, Bob will have 5 cents more than Albert. If Albert then gives Bob another 20 cents, twice Albert's amount will exceed Bob's amount by 5 cents. How mu

Algebra ->  Expressions-with-variables -> SOLUTION: If Albert gives Bob 10 cents, Bob will have 5 cents more than Albert. If Albert then gives Bob another 20 cents, twice Albert's amount will exceed Bob's amount by 5 cents. How mu      Log On


   

Question 697604: If Albert gives Bob 10 cents, Bob will have 5 cents more than Albert. If Albert then gives Bob another 20 cents, twice Albert's amount will exceed Bob's amount by 5 cents. How much money did each boy have at first?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
If Albert gives Bob 10 cents, 
Albert will have A-10 cents and Bob will have B+10
Bob will have 5 cents more than Albert. 

So what Bob will have equals what Albert will have PLUS 5 cents

B+10 = A-10 + 5
simplifying
B+10 = A-5
B+15 = A

If Albert then gives Bob another 20 cents, 
Albert will have A-10 - 20 cents and Bob will have B+10 + 20

Simplifying

Albert will have A-30 cents and Bob will have B+30

twice Albert's amount will exceed Bob's amount by 5 cents. 
So 2 times (A-30) will equal B+30 PLUS 5

or

2(A-30) = B+30 + 5

or

2A-60 = B+35
   2A = B+95

So we have this system:

B+15 = A
2A = B+95

Solve it and get Albert had 80 cents and Bob had 65 cents.

Checking:

If Albert gives Bob 10 cents, Bob will have 75 cents and Albert will
have 70 cents

5 cents more than Albert. 
That checks since 80 is 5 more than 75.

If Albert then gives Bob another 20 cents, 
Then Albert will have 50 cents and Bob will have 95 cents

twice Albert's amount will exceed Bob's amount by 5 cents. 
That checks because twice 50 cents is a dollar which is
5 cents more than Bob's 95 cents.

Edwin