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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]
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Carcass wrote:
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8

(B) 12

(C) 16

(D) 20

(E) 24


Let x = the ORIGINAL price per orange

If the price is lowered by 40%, then consumers will pay 60% of the original price.
In other words, the REDUCED price per orange = 60% of x = 0.6x

Given: When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price.
Let's start with a word equation: (number of oranges purchased with $12 at REDUCED price) = (number of oranges purchased with $12 at ORIGINAL price) + 4
Substitute to get: 12/0.6x = 12/x + 4
Multiply both sides by x to get: 12/0.6 = 12 + 4x
Simplify to get: 20 = 12 + 4x
Subtract 12 from both sides: 8 = 4x
Solve: x = 2
So the ORIGINAL price is $2 per orange.

How many oranges can be purchased for 24 dollars at the original price?
Number of oranges that can be purchased = 24/2 = 12

Answer: B

Cheers,
Brent
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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]
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