SOLUTION: If you have to pay $75.00 and have 27 bills of $1.00 and $5.00, how many bills do you need of $1.00 and $5.00 to pay.

Question 965860: If you have to pay $75.00 and have 27 bills of $1.00 and $5.00, how many bills do you need of $1.00 and $5.00 to pay.
Found 3 solutions by CubeyThePenguin, ikleyn, greenestamps:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
x = number of $1 bills
y = number of $5 bills

x + y = 27
x + 5y = 75

Multiply equation 1 by 5.

5x + 5y = 135
x + 5y = 75

Subtract to get 4x = 60 and x = 15.

You need 15 one-dollar bills and 12 five-dollar bills.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Based on common sense, it is not required to use all 27 bills to pay.

The problem formulation is out of the common sense.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The language use in the statement of the problem is definitely poor, leaving the problem open to different interpretations. With one interpretation of the problem, you could pay the $75 with 15 $5 bills and still have 12 bills (of either $1 or $5 denominations) left.

Assuming the intent of the problem is to use exactly all 27 bills to make the payment, the solution by the other tutor is a good typical algebraic solution.

You can get good mental exercise by solving a problem like this using logical reasoning and simple mental arithmetic, perhaps like this:

The total to be paid is $75; since any number of $5 bills makes a total that is a multiple of $5, the total value of the $1 bills must also be a multiple of 5. So the number of $1 bills is either 5, 10, 15, 20, or 25.

Then a few quick mental calculations show the correct total is with 15 $1 bills: 15($1)+12($5) = $15+$60 = $75

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