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