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designermamajessica
06-24-2009, 06:30 PM
Pencils and pens are on sale. Pencils sell for 96 cents a dozen and pens sell for 51 cents for 3. Karen bought some of each. How many pencils did she buy if she spent \$2.47?

I just do not get how to set this problem up?

Any help would be greatly appreciated.

galactus
06-24-2009, 06:48 PM
Since the problem does not say how many she bought in all, we have one equation with two unknowns.

The pens cost .96/.12=.08 dollars each

The pencils cost .51/3=.17 dollars each.

She spends 2.47

Let x= the number of pens and y=the number of pencils.

.08x+.17y=2.47

Try some values until you get an integer solution. HINT: Let the number of pencils be 7.

designermamajessica
06-24-2009, 07:02 PM
Thanks that is what I had, I just did not know how to solve for two unknowns without just guessing and filling in the blank.

So what if you were given the total number of pens and pencils sold with the dollar amount, how would you write that out? I don't have a question like that right now but I know somewhere down the line I will get asked.

galactus
06-24-2009, 07:05 PM
Well, if they would have said, "she bought 23 pens and pencils total" as well as the cost given, then we could have set it up like so:

x+y=23....[1]

.08x+.17y=2.47.........[2]

Solve [1] for y:

y=23-x

Sub into [2] and solve for x:

.08x+.17(23-x)=2.47

x=16 and y=7