brain teaser

A girl has exactly enough money to buy 3 sweaters and 2 skirts, or to buy 3 skirts and no sweaters. How many sweaters can she buy is she buys only one skirt

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1. number of sweaters ---- x
number of skirts ------- y

3x + 2y = 3y
3x = y or x = y/3

so she has 3y to spend
if she buys 1 skirt, or she spends y, that leaves her with 2y
but y = 3x, so 2y = 6x = 6 sweaters

check:
suppose she has \$90
so she can buy 3 skirts, each skirt would cost \$30
but 3 sweaters + 2 skirts cost \$90
3x + 60 = 90
3x = 30
x = 10
each sweater would cost \$10.

so if she buys only 1 skirt, she would have
90-30 or \$60 left, for which she could buy 6 sweaters, as shown above.

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posted by Reiny

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