SOLUTION: A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the number of 15-

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Question 500675: A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the number of 15-cent stamps is 5 more than one half the number of 10 cent stamps, how many stamps of each denomination did the student obtain?
This is as far as I got (chart form):
# of stamps Denomination Value
5 cent n+2 .05 .5n+10
10 cent n .10 .10n
15 cent (1/2n)+5 .15 .15(1/2n)+5
I am suppose to get the answer of:
28 5 cent stamps, 26 10 cent stamps, and 18 15 cent stamps. I have tried this problem numerous ways and cannot get to the whole numbers listed above.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


So far, you have it exactly right.

The next step is to add all of the values. The value of the 10 cent stamps is, as you said, , the value of the 5 cent stamps is and the value of the 15 cent stamps is

These three values add up to the total value of the stamps, namely $6.70.

Now, since I hate decimal fraction coefficients, I'm going to change everything from dollars and fractions of dollars to whole number of cents. First,, $6.70 is nothing more than 670 cents, and the three values of the individual denominations become , , and . Now add it all up:



First let's get rid of the parentheses:



And then get the RHS constants over into the LHS by adding the opposites:



But we still have that pesky fraction -- with a denominator of 2. Multiply by 2:



Collect the terms in the RHS:



Can you get it from here, remembering that represents the number of 10-cent stamps?

John

My calculator said it, I believe it, that settles it
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