SOLUTION: A man spent P6.00 for a certain set of items. If the price per item were increased by 10 cents, he could have bought two less items for the same amount of money. How many items

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Question 1186988: A man spent P6.00 for a certain set of items. If the price per item were
increased by 10 cents, he could have bought two less items for the same
amount of money. How many items were bought and at what price per item?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the price, in dollars.


The condition says

    6%2Fx - 6%2F%28x%2B0.1%29 = 2.


To simplify, divide both sides by 2

    3%2Fx - 3%2F%28x%2B0.1%29 = 1.    (1)


At this point, you may guess the answer MENTALLY:  x = 0.50 dollars per item.


ANSWER.  The price per item is $0.50.  The number of items bought is  3%2F0.50 = 6.


CHECK.  I will check equation (1).


        Its left side is  3%2F0.5 - 3%2F0.6 = 6 - 5 = 1.    ! Correct !

Solved.

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Alternatively, you can solve the problem algebraically, by reducing equation (1)
to the standard quadratic form.