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Question 964370: the price of oranges increase by 13.33% you have four oranges less for a rupee. how many oranges can now be had for a rupee?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have two equations.
x*p = 1 is the first equation.
x represents the number of oranges and p represents the price per orange.
13.33% divided by 100 is equal to .1333.
1.1333 * p * (x-4) is the second equation.
the price of oranges went up 13.33% which means the new price of oranges is equal to 1.1333 * p.
the number of oranges that can be bought with 1 rupee is now x-4 rather than s.
your 2 equations are:
x*p = 1
(x-4)*(1.1333*p) = 1
these equations need to be solved simultaneously.
simplify the second equation to get:
x*1.1333*p - 4*1.1333*p = 1
in the first equation of x*p = 1, you can solve for p to get p = 1/s.
replace p with 1/x in the second equation to get:
x*1.1333*p - 4*1.1333*p = 1 becomes x*1.1333*1/x - 4*1.1333*1/x = 1
multiply both sides of this eqution by x to get:
1.1333*x - 4*1.1333 = x
subtract x from both sides of the equation and add 4*1.1333 to both sides of the equation to get:
1.1333*x - x = 4*1.1333
simplify to get:
.1333 * x = 4*1.1333
divide both sides of this equation by .1333 to get:
x = 4*1.1333/.1333
solve for x to get x = 34.00750188.
round this off to 34.
x is the number of oranges.
in the equation of x*p = 1, replace x with 34 to get 34*p = 1.
solve for p to get p = 1/34.
he can buy 34 oranges at 1/34 of a rupee apiece.
if the price goes up by 13.33%, then the new price is 1/34 * 1.1333 = .0333323529 rupees.
the number of oranges goes down from 34 to 30.
.0333323529 * 30 = .9999705882 which is very close to 1, so the solution is confirmed as good.
when the price goes up 13.33%, he can get 30 oranges with one rupee.
at the original price, he can get 34 oranges.
the numbers don't work out exactly because the 13.33% is a truncated version of 13.333333333333333333% which is equal to 200/15.
the decimal equivalent of that is 2/15 which is equivalent to .13333333333333.
if you used that number instead, then the numbers would have come out exactly.
if you were confused by the fact that the numbers didn't come out as integers, that's the reason.
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