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Don has five, tens, and twenties

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?

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