SOLUTION: Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?

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Question 1174007: Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52750)   (Show Source): You can put this solution on YOUR website!
.

x fancy shirts and 7-x plain shirts.


Total money equation


    28x + 15*(7-x) = 131   dollar.


Solution


    x =  = 2.


ANSWER.  2 fancy and 7-2 = 5 plain shirts.

Solved.



Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


The other tutor showed a good typical formal algebraic solution.

You can get a lot of valuable mental exercise by solving the problem informally, using logical reasoning and simple arithmetic.

(1) $131 for 7 shirts makes the average cost about $18.70. Since that is much closer to $15 than to $28, most of the shirts must be the less expensive plain shirts.

(2) The cost of each fancy shirt is $28, so the cost of any number of fancy shirts is an even number. Since the cost of each plain shirt is an odd number, and the total cost of all the shirts is an odd number, the number of plain shirts must be odd.

Either one of those alone, or both together, would lead to the guess that she bought 5 plain shirts and 2 fancy shirts. And trying that combination shows it is the right one: 5(15)+2(28) = 75+56 = 131.
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