Jasmine cashes out her drawer at the end of her shift and finds she has $165 in $5 and $10 bills. If the total number of bills is 21, how many of each type of bill does Jasmine have?

Answer 1

Hi Michael!

This is a classic system of equations problem, where you must find at least 2 relevant equations that represent the problem, and then use that to derive an answer.

If we let x be the number of $5 bills and y be the number of $10 bills, then how can we represent the statement that the total number of bills is 21?

x + y = 21 (equation 1)

Then, we can use the same variables to represent the statement that there is a total of $165.

5x + 10y = 165 (equation 2)

Now, we have two equations with the same variables, and we can simply solve for them in a system of equations.

Multiply the equation 1 by 5:

5x + 5y = 105 (equation 1 multiplied by 5)

And subtract from equation 2:

5x + 10y = 165

5x + 5y = 105

To get:

5y = 60

Which means y = 12.

Using this information, and knowing from equation 1 that x + y = 21, we can plug in 12 for y and solve for x:

x + 12 = 21

So we get that:

x = 9

The answer is, Jasmine has NINE $5 bills and TWELVE $10 bills.

---

A quick check to make sure that that adds up to $165:

9($5) + 12($10) = $45 + $120 = $165.

Answer 2

x = number of $5 bills

21 - x = number of $10 bills

21 bills total

values of five dollar bills + value of 10 dollar bills = total value:

x * 5 + (21-x)*10 = 165

5x + 210 - 10x = 165

-5x = -45

x = 9 = number of $5 bills

21 x = 21 - 9 = 12 = number of $10 bills