SOLUTION: a store charges $21 or six boxes of cookies . A second store charges $15 for five boxes of cookies but you have to buy a gallon of milk for two dollars to get that deal . Right to

Question 1130025: a store charges $21 or six boxes of cookies . A second store charges $15 for five boxes of cookies but you have to buy a gallon of milk for two dollars to get that deal . Right to cost model equations for both stores and find the number of boxes of cookies that makes the cost equals .
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!

First Store:
customer must buy increments of 6 boxes.

Second Store:
The cost for the milk must be included but the emphasis is on the boxes of cookies;

customer must buy increments of 5 boxes.

17*6 boxes at first store should match the cost of 21*5 boxes at second store.
That is, 102 boxes at the first store should be same cost as 105 boxes at the second store.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The grammar and spelling in the statement of the problem make the problem unclear. It sounds as if we are supposed to find a number of boxes of cookies so that same number of boxes of cookies at the two stores will cost the same. But that will never happen with the given prices.

So I will guess that the problem is supposed to be to find two DIFFERENT numbers of boxes of cookies for which the costs of the cookies at the two stores will be the same.

In that case, note that the purchases at the first store are in increments of $21 (for 6 boxes of cookies) and the purchases at the second store are in increments of $17 ($15 for 5 boxes of cookies, plus $2 for the gallon of milk).

If the costs in the two stores are to be the same, that cost must be a common multiple of 17 and 21. Since 17 and 21 are relatively prime, the least common multiple of 17 and 21 is 17*21 = 357.

So 17 purchases each at the first store, consisting of 17*6 = 102 boxes of cookies, will cost the same as 21 purchases at the second store, consisting of 21*5 = 105 boxes of cookies and 21 gallons of milk.
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