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Sally purchased notebooks at \$2.50 apiece, and pens at \$1.00 apiece. If she bought a total of 12 items for \$24.00, how many notebooks did she buy?

Sally purchased notebooks at \$2.50 apiece, and pens at \$1.00 apiece. If she bought a total of 12 items for \$24.00, how many notebooks did she buy?

Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
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Sally purchased notebooks at \$2.50 apiece, and pens at \$1.00 apiece. If she bought a total of 12 items for \$24.00, how many notebooks did she buy?
The equations area:
x+y=12; x=number of notebooks and y= number of pens
2.5x + y = 24
Y=24 - 2.5x
x + 24 - 2.5x =12
12 = 1.5x
x=8 notebooks
y = 4 pens

4.9 4.9 (63 lesson ratings) (63)
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Anthony, we are going to have to come up with two equations and do some substitution.

Let's say that n= the number of notebooks and p= the number of pens.

We are given that a total of 12 items were bought, so n+p=12.

Using the prices that we have, our second equation is 2.50n+1.00p=24.00 remembering that we can take off zeroes to make our work easier and that 1 times anything is itself, we can write the equation as

2.5n+p=24

Now, going back to the first equation, since p is alone in the second equation, let's solve for p in the first.  We get that p=12-n.

Subsitute this "value" for p in the second equation.  We end up with

2.5n+(12-n)=24, or 2.5n+12-n=24

Combining like terms, we get 1.5n+12=24.  1.5n=12, so n=8.

She bought 8 notebooks.