Marty made a $220 bank deposit using $10 bills and $5 bills. she gave the teller a total of 38 bills, how many $5 bills were in the deposit?
a) 6 five-dollar bills
b) 28 five-dollar bills
c) 32 five-dollar bills
d) 34 five-dollar bills

ANSWER: 32 five-dollar bills

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EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

Divide both sides of equation (II) by 5 so our numbers become smaller

Rearrange (I) to solve for y so that we can substitute into (II)

Substituting this into equation (II) for the y:

We have 32 five-dollar bills

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If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

32 five-dollar bills and 6 ten-dollar bills