SOLUTION: A student who has d dimes and n nickels buys P pencils at 7 cents each. How many cents does the student have left?

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Question 612887: A student who has d dimes and n nickels buys P pencils at 7 cents each. How many cents does the student have left?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Probably the reason you found this problem difficult is the fact that the problem uses variables for several of the numbers. I think that if you had numbers for the d, n and p then this would be easy.

For example, if the problem was: "A student who has 8 dimes and 3 nickels buys 12 pencils at 7 cents each. How many cents does the student have left?", wouldn't this be easy? I hope that you would know you would
  1. Find the amount of money the student had by
    1. Multiplying the number of dimes by 10 to get the value of those dimes
    2. Multiply the number of nickels by 5 to get the value of the nickels
    3. Add the value of the dimes and the value of the nickels to get the total amount he/she has to spend
  2. Multiply the number of pencils the student bought by 7 to find the total amount spent.
  3. Subtract the money the student spent from the total he/she had. This would be how much is left.

This is the underlying logic of this problem. The "trick" is to understand that the logic stays the same no matter what the numbers look like! The logic stays the same whether the numbers are expressed as whole numbers, fractions, decimals, square roots, variables, weird expressions, etc.

So the value (in cents) of some dimes is, as always, the number of dines times 10. In this problem the value of the dimes is:
d * 10 or 10d
The value (in cents) of some nickels is, as always, the number of nickels times 5. In this problem the value of the nickels is:
n * 5 or 5n
The total amount of money (in cents) the student has is the value of the dimes plus the value of the nickels:
10d + 5n
The total amount spent (in cents) is the number of pencils times the cost of each pencil:
p * 7 or 7p
And the amount left (in cents) will be the total spent subtracted from the total amount of money the student had:
(10d + 5n) - 7p
or just
10d + 5n - 7p
This is the answer to your problem!
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