SOLUTION: A bank teller cashes a check for $1500 using a certain number of $1 bills, ten times as many $5 bills, a certain number of $10 bills, and twice as many $50 bills. How many of each

Question 1142728: A bank teller cashes a check for $1500 using a certain number of $1 bills, ten times as many $5 bills, a certain number of $10 bills, and twice as many $50 bills. How many of each did the teller use?
A = $1
B = $5
C = $10
D = $50
$1500 = A + 10B + C + D2
Not sure. Non-homework.

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39627) (Show Source): You can put this solution on YOUR website!
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$1500 using a certain number of $1 bills, ten times as many $5 bills, a certain number of $10 bills, and twice as many $50 bills.
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A of $1's
B of $5's
C of $10's
D of $50's
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BILLS COUNT DOLLARS ONES A A FIVES 10A 5*10A TENS C 10C FIFTIES 2C 50*2*C Total Money 1500

The money account equation, once simplified will be equivalent to ;
Recheck in case any mistake was made.
Only few solutions for the equation. Only whole numbers are allowed.

You could try graphing but might be easier to ...

..., Pick whole-number values for C from 0, through 13 and check if A is a whole number or not.

You should find that the solution is C=9 and A=10. ......
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

Let x be the number of $1 bills; then 10x is the number of $5 bills.

Let y be the number of $10 bills; then 2y is the number of $50 bills.

The total value of the bills is

The total value is given as $1500:

Use some logical reasoning to solve this quickly, knowing that x and y are positive integers (or possibly non-negative integers).

"110y" and "1500" are both multiples of 10; that means "51x" has to be a multiple of 10. And that of course means x is a multiple of 10.

And trying x=10 gives you a solution in integers, so that is the solution:

ANSWER:
$1 bills: x = 10
$5 bills: 10x = 100
$10 bills: y = 9
$50 bills: 2y = 18 CHECK: 10(1)+100(5)+9(10)+18(50) = 10+500+90+900 = 1500
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