Don has five, tens, and twenties

Question

B.K. has $200 in fives, tens, and twenties. The number of $20 bills is one-third the number of $5 bills. The number of $10 bills is 1 greater than twice the number of &5 bills. How many of each type of bill does she have?

Answer 1

I tried to post an answer to this before so sorry if this ends up as a double response.

Since they give all amount of bills in relation to $5 bills that should be the variable of choice.

Let x = number of $5 bills

Then 1/3x = # of $20 bills

and 2x + 1 = # of $10 bills

Here's where things get a little tricky, now instead of using $200 you need to know the number of $5 bills necessary to make $200.

200/5 = 40

Lastly, you need to account for the differences in the number of $5 bills necessary to make the other 2 denominations.

$10/$5 = 2

$20/$5 = 4

So, the equation you end up with is:

1x + 2(2x+1) + 4(1/3x) = 40

Multiplying that out yields

x+ 4x + 2 +(4/3)x = 40

Simplified to (19/3)x + 2 = 40  ---------> multiply by 3 on both sides to get

19x + 6 = 120 ----------------> subtract by 6 on both sides to get

19x = 114 ------------------> divide by 19 and...

x = 6

Now substitute in for the remaining values:

# of $10 = 2(6) +1 = 13

# of $20 = 1/3(6) = 2

To check, make sure the total adds up to $200

(6*$5) + (13*$10) + (2*$20) = $200