# A man bought some apples at a certain price. Find price per 100 apples

A man was asked what price per 100 he paid for some apples, and his re-

ply was as follows: “If they had been 4¢ more per 100 I should have got five

less for $1.20.” Can you say what was the price per 100?

goli202084 Answered question

Let's assume that the price per 100 apples is x¢ and the man bought y apples then we have eq. 1) as x*y = 1.2$ Man said, if the price per 100 was 4¢ more, then he could have had 5 less from what he bought, thus eq. 2) - (x+4)*(y-5) = 1.2$ x is in cents in both the equations and the price x is per 100 apples, so updated equations become x y __ x ___ = 1.2 --------(1) 100 100 (x+4) (y-5) ____ x _____ = 1.2 --------(2) 100 100 Solving equations 1 and 2 eq(1) => xy = 12000 => y=12000/x ---- (3) Solving equation 2 we get, xy-5x+4y-20 = 12000 Substituting xy=12000 in above equation => -5x+4y = 20 Again substituting y=12000/x in above equation, -5x+48000/x = 20, dividing both sides by 5 -x+9600/x = 4 => x^2+4x-9600 = 0 => (x+100)(x-96) = 0 this gives 2 solutions x=96 and x=-100 Discarding -ve value of 100 Final answer, man bought, 100 apples for 96 cents.

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