SOLUTION: A grocery store sells bags of chips for $4 each and bottles of pop for $2.75 each. A student goes into the grocery store to buy chips and pop. She buys 15 items for a total of $5

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Question 1156426: A grocery store sells bags of chips for $4 each and bottles of pop for $2.75 each.
A student goes into the grocery store to buy chips and pop. She buys 15 items for
a total of $50. How many bags of chips and how many bottles of pop did she
buy? Make sure to show all you work. Make sure to introduce your variables,
you may want to use ( c for chips and p for pop)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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bags of chips for $4 each and bottles of pop for $2.75 each.
A student goes into the grocery store to buy chips and pop. She buys 15 items for
a total of $50.
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system%28c%2Bp=15%2C4c%2B2.75p=50%29

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4%2815-p%29%2B2.75p=50---------using substitution, for one equation in one variable...

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @josgartihmetic sets up the problem in the usual way using two variables:
c+p = 15
4c+2.75p = 50

She then suggests solving the problem using substitution. That is a perfectly good algebraic method; but when the two equations are in this form, elimination is much easier.

Multiply the first equation by 4 and then compare the two equations using subtraction:
   4c + 4p    = 60
   4c + 2.75p = 50
  -----------------
        1.25p = 10
            p = 10/1.25 = 8

ANSWER: 8 bottles of pop and 15-8=7 bags of chips

If a formal algebraic solution is not required, you can get the answer much faster with a little logical reasoning and mental arithmetic -- and using virtually the same calculations. It goes like this:

(1) If all 15 items were bags of chips, the cost would be 15 times $4, or $60. That is $10 more than the actual cost.
(2) Each bottle of pop costs $1.25 less than each bag of chips.
(3) To bring the cost down $10 from $60 to $50, the number of bottles of pop must be $10 divided by $1.25, which is 8.

And again the answer is 8 bottles of pop and 7 bags of chips.