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

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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 $1.20.” Can you say what was the price per 100? Answered question ### 1 Answer 0 Let's assume that the price per 100 apples is x¢ and the man bought y apples then we have eq. 1) as x*y = 1.2$
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
Final answer, man bought, 100 apples for 96 cents.