problem 249 mathcounts

Mathematics
Tutor: None Selected Time limit: 1 Day

Sam went to the bank to withdraw $440.00. He received 30 bills altogether. There were some 5-,some 10- and some 20-dollar bills. Sam received 4 times as many 20-dollar bills as 5-dollar bills. How many 10-dollar bills did Sam receive?

Oct 12th, 2014

Let x = number of 5-dollar bills

Then 4x = number of 20-dollar bills

and number of 10 dollar bills = 30 - x -4x = 30 - 5x

Total value of bills = 5 * x + 4x * 20 + (30 -5x) *10

                              =5x + 80x +  300 - 50x

                             =35x + 300 dollars

But this must equal $440

35x + 300 = 440

35x = 140

x= 140/35 = 4

He received 4  five- dollar bills

He received 4 * 4 = 16  twenty - dollar bills

So he received 10  ten- dollar bills

( check : 20 + 320 + 100 = 440 dollars)


Oct 12th, 2014

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