SOLUTION: Malcome has $1043 in bills of the following denominations: hundreds,fifties,twenties,fives,and ones. He has three times as many fifties as hundreds,twelve times as many twenties a

Question 126501: Malcome has $1043 in bills of the following denominations: hundreds,fifties,twenties,fives,and ones. He has three times as many fifties as hundreds,twelve times as many twenties as hundreds, and four times as many ones as hundreds. He has nine more fives than hundreds. How many of each denomination of bill does he have?
Answer by marcsam823(57) (Show Source): You can put this solution on YOUR website!
1. Define values for the number if bills of each denomination (given in the problem):
Let x = number of $100 bill
Let 3x = number of $50 bills
Let 12x = number of $20 bills
Let 4x = number of $1 bills
Let x+9 = number of $5 bills
2. Define values for the dollar values of each denomintion (multiply variable from step 1 by the value of the denomiation):
Let 100x = value of all $100 bills
Let 50(30x) = 150x = value of all $50 bills
Let 20(12x) = 240x = value of all $20 bills
Let 1(4x) = 4x = value of all $1 bills
Let 5(x+9) = 5x+45 = value of all $5 bills
3. Set up the equation:

4. Simplify and solve:

5. Substitute x = 2 for all variables in step 1 to determine number of each denomination Malcolme has:
$100 bills
$50 bills
$20 bills
$1 bills
$5 bills
6. Check: Multiply the number of each bill by its face value and sum:

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