Feb. 9, 2005
Raincoat, Hat, and Boots
A raincoat, hat, and boots were bought for $280. The raincoat cost $180 more than the hat, and the hat and the raincoat together cost $240 more than the boots.
How much did each item of raingear cost?
MathGolf: Challenge 20
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If instead of the raincoat, hat, and boots only two pairs of boots were bought, the price would not be $280, but $240 less. Thus, the two pairs of boots cost $280 $240 = $40. Hence, one pair cost $20.
Now, we find that the raincoat and hat together cost $280 $20 = $260, the raincoat costing $180 more than the hat. If instead of the raincoat and hat we could buy two hats, and we would pay not $260 but $180 less, that is, $260 $180 = $80. Hence, one hat costs $40.
Thus, the prices of the items of raingear were as follows: boots $20; hat $40; and raincoat $220.
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