story problem

Question

You have 13 bills in your wallet in $1, $5, and $10. There are twice as many $1 bills as $5 bills. The number of $10 bills is one more that the number of $5 bills. How many of each bill do you have? How much money do you have?

Answer 1

Hi Alissa.

 

I tried to do this with "algebra" but kept getting non-integer bills - So I just started playing with the numbers.  The key is the $5 bills.  All the other bills reference the $5 bills.

 

If we have 1 $5 bill, we must have 2 $10 bills.  And that means we have 2 $1 bills because we have twice as many $1's as we do $5's.   This adds up to 1+2+1 = 4 bills.  Not enough.

 

Say  instead we have 2 $5 bills.   We must have 3 $10 bills and 4 $1 bills.

This adds up to 2+3+4=9 bills.  Not enough.

 

Try 3 $5 bills.  Requires 4 $10 bills and 6 $1 bills.

This adds up to 3+4+6=13.  BINGO!

 

So we have 3 $5 = $15

We have 4 $10 = $40

We have 6 $1 = $6

 

All together we have $15+$40+$6 = $61