A cash register contains $20 bills and $50 bills with a total value of $610. If there are 17 bills total, then how many of each does the register contain?

number of twenty dollar bills = 8

number of fifty dollar bills = 9

Work Shown:

T = number of twenty dollar bills

F = number of fifty dollar bills

T+F = 17, since there are 17 bills total

T+F-T = 17-T ... subtract T from both sides

F = 17-T we'll use this later

20T = value of all of the twenty dollar bills

50F = value of all the fifty dollar bills

20T+50F = total value in dollars

20T + 50F = 610

20T + 50(17 - T) = 610 plug in F = 17 - F

20T + 50(17) + 50(-T) = 610 distribute

20T + 850 - 50T = 610

-30T + 850 = 610

-30T + 850 - 850 = 610 - 850 subtract 850 from both sides

-30T = -240

-30T/(-30) = -240/(-30) ... divide both sides by -30

T = 8

F = 17 - T

F = 17 - 8

F = 9

we have T = 8 twenties and F = 9 fifties

20T = 20*8 = 160 dollars with just the twenty dollar bills

50F = 50*9 = 450 dollars with just the fifty dollar bills

160+450 = 610 dollars total

This confirms the answer.

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