Question 1202534: Marcel has a jar filled with one and five dollar bills. The jar contains 34 bills and totals $110. How many bills of each type does he have?
Number of one dollar bills
Number of five dollar bills
Found 4 solutions by Theo, Alan3354, josgarithmetic, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of 1 dollar bills.
y = number of 5 dollar bills.
jar contains 34 bills
x + y = 34
total money in the jar is 110 dollars.
x + 5y = 110
solve for y in the first equqtion to get:
y = 34 - x
replace y in the second equation with tha to get:
x + 5 * (34 - x) = 110
simplify to get:
x + 170 - 5x = 110
combine like terms to get:
-4x + 170 = 110
add 4x to both sides of the equation and subtract 110 from both sides of the equation to get:
60 = 4x
solve for x to get:
x = 15
since x + y = 34, then y must be equal to 19.
x + y becomes 15 + 19 which is equal to 34.
x + 5y becomes 15 + 95 which is equal to 110.
values look good.
solution is he has 15 one dollar bills and 19 five dollars bills.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Marcel has a jar filled with one and five dollar bills. The jar contains 34 bills and totals $110. How many bills of each type does he have?
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N + F = 34 --- # of bills
N + 5F = 110 --- sum of bills
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Can you do the rest?
Answer by josgarithmetic(39617)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You have three responses showing formal algebraic solutions. Assuming you are studying algebra, you should understand those solutions.
But you can get good mental exercise, and good problem-solving practice, by solving the problem informally, using logical reasoning and simple mental arithmetic.
Here is a way to solve any problem like this informally.
(1) If all 34 bills were $1 bills, the total would be $34.
(2) The actual total is $110, which is $76 more than $34.
(3) The difference between the value of a $5 bill and a $1 bill is $4.
(4) The number of $5 bills needed to make up the additional $76 is $76/$4 = 19.
ANSWER: 19 $5 bills; and 34-19 = 15 $1 bills
CHECK: 19($5)+15($1) = $95+$15 = $110
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