SOLUTION: A school cafeteria cashier has collected $243 in one-dollar, five-dollar, and ten-dollar bills. The number of one-dollar bills is eight more than 20 times the number of ten-dolla

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Question 1192263: A school cafeteria cashier has collected $243 in one-dollar, five-dollar,
and ten-dollar bills. The number of one-dollar bills is eight more than 20
times the number of ten-dollar bills. The cashier also has seven more
than twice the number of ten-dollar bills in five-dollar bills. How many
bills of each value does the cashier have?
Answer by ikleyn(52786) About Me  (Show Source):
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A school cafeteria cashier has collected $243 in one-dollar, five-dollar,
and ten-dollar bills. The number of one-dollar bills is eight more than 20
times the number of ten-dollar bills. The cashier also has seven more
than twice the number of ten-dollar bills in five-dollar bills. How many
bills of each value does the cashier have?
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Let x be the number of the ten-dollar bills.

Then the number of one-dollar bills is (8+20x)

and  the number of five-dollar bills is  (7+2x).


Now write the total money equation

    243 = 10x + (8+20x) + 5*(7+2x).


Simplify and find x

    243 = 10x + 8 + 20x + 35 + 10x

    243 = 40x + 43

    40x = 243 - 43

    40x =    200

      x =    200/40 = 5


ANSWER.  5 ten-dollar bills;  (8+20*5) = 108 one-dollar bills  and  (7+2*5) = 17 five-dollar bills.


CHECK.  5*10 + 108*1 + 17*5 = 243  total money.    ! Correct !

Solved.

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In a joking form, this problem is about finding three unknowns using only one equation . . .