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Something wrong here. If two jackets cost $180 but two of each of the items together cost $170, that’s less than the cost of two jackets by themselves! They must be giving things away!

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1 Answer

Although there is something wrong with the question, because two jackets could not cost more than two jackets plus other items, it is possible to come up with solutions.

Let H=cost of hat, T=cost of T-shirt, and J=cost of jacket, we can write two equations:

3H+2S+J=140,

2H+2S+2J=170,

assuming the first two statements are correct.

If we subtract the first equation from the second we get:

-H+J=30, so H=J-30, that is, the hat is $30 cheaper than the jacket.

Substitute for H in the second equation:

2(J-30)+2S+2J=170,

2J-60+2S+2J=170,

4J+2S=230, which simplifies to 2J+S=115, and S=115-2J.

So we now have S and H in terms of J.

We know that all costs are positive so 115-2J>0, 115>2J, $57.50>J, that is, the jacket costs no more than $57, if we assume whole dollars. This gives a starting point for the table.

If we assume that a T-shirt costs less than a hat, which costs less than a jacket, we can write the following table:

S is less than H is less than J, cost of two jackets

 1                     27                   57            114

 3                     26                   56            112

 5                     25                   55            110

 7                     24                   54            108

 9                     23                   53            106

11                    22                   52            104

13                    21                   51            102

15                    20                   50            100

17                    19                   49              98

using the formulas: H=J-30 and S=115-2J. All these costs fit the first two equations. My guess is that two $54 jackets cost $108 not $180, in which case, the T-shirt costs $7 and the hat $24.

by Top Rated User (1.1m points)

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