Question 874979: Three of Carlos’ and Amy's friends are purchasing school supplies at the bookstore.Stan buys a notebook, three packages of pencils and two markers for $7.50.
Jan buys two notebooks, six
packages of pencils and five markers for $15.50.
Fran buys a notebook, two packages of pencils and
two markers for $6.25. How much do each of these three items cost?
Explain in words or with symbols how you can use your intuitive reasoning about these purchases
to find the price of each item.
Note:so far I've tired the following prices and they did not work notebook:$1.25,$1.30,$1.00,Package of pencils:$1.50 Markers:$1.00,0.50,0.80
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let n be notebooks, p be packages of pencils, m be markers, then
Stan n + 3p + 2m = $ 7.50
Jan 2n + 6p + 5m = $15.50
Fran n + 2p + 2m = $ 6.25
let's subtract Fran from Stan and we get
p = $1.25
rewrite the three equations substituting for p
Stan n + 3(1.25) + 2m = 7.50
Jan 2n + 6(1.25) + 5m = 15.50
Fran n + 2(1.25) + 2m = 6.25
rewrite the three equations now with 2 variables
Stan n + 2m = 3.75
Jan 2n + 5m = 8.00
Fran n + 2m = 3.75
Note that Fran and Stan are the same now, so we use only one
Stan/Fran n + 2m = 3.75
Jan 2n + 5m = 8.00
now we multiply Stan/Fran by 2
Stan/Fran 2n + 4m = 7.50
Jan 2n + 5m = 8.00
now subtract Stan/Fran from Jan
m = $.50
we now have p = $1.25 and m = $.50
let's substitute in Stan to get n
n + 3(1.25) + 2(0.50) = 7.50
n + 4.75 = 7.50
n = $2.75
therefore we have the following
n = $2.75, p = $1.25, m = $.50
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