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

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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) About Me  (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 51A%2B110C=1500;
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 ...
51A=1500-110C
highlight_green%28A=%281500-110C%29%2F51%29

..., 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) About Me  (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

1%28x%29%2B5%2810x%29%2B10%28y%29%2B50%282y%29+=+51x%2B110y

The total value is given as $1500:

51x%2B110y+=+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:

51%2810%29%2B110y+=+1500
110y%2B510+=+1500
110y+=+990
y+=+9

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