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Date: 08/21/97 at 13:11:47
From: Anonymous

Dr. Math,

I am an adult who is taking a correspondence course in Algebra I.
I have the following question, and the textbook has not addressed this
kind of problem. If you could please guide me through the steps of
solving it, I would be very appreciative.

A man purchases some .02 and some .15 cent stamps at the same time.
He pays \$1.56 for all the stamps.  There are 10 more .02 stamps than
.15 stamps.  How many of each kind did he buy?

Thanks,
Sherell
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Date: 08/22/97 at 15:04:27
From: Doctor Beth

Okay, we'll have to decide to let a variable equal something, perhaps
the number of .15 stamps.

If x is the number of .15 stamps we buy, then the number of .02 stamps
is 10 more, so it's x + 10.

When the man purchases the stamps, he spends \$1.56, but we also know
that he spends .15x + .02(x+10), because the amount spent is the
number of stamps times the price of each stamp. So now we have the
equation

1.56 = .15x + .02(x+10)
To solve for x, first I'll
multiply and get
1.56 = .15x + .02x + .2
Now I'll combine .15x and .02x
to get .17x, and subtract the
.2 from both sides, to get
1.36 = .17x

Dividing both sides by .17 gives us

8 = x

So now we know that 8 = x, but we're not quite done - we have to make
sure that we're answering the question in the problem. Since x was the
number of .15 stamps, the man purchased 8 of the .15 stamps. The
number of .02 stamps that he bought was x+10, so it must be 18.

15 cents each, and then buy 18 stamps that each cost 2 cents, that you
spend \$1.56.

-Doctor Beth,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Algebra
Middle School Word Problems

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