farukqmul 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

We use the equation: price per item x no. of items = total cost. Here, we let p = the original price of an orange and q = the original number of oranges purchased. We can create the equation for the original total cost:

pq = 12

q = 12/p

After the orange’s price is lowered, we have that 0.6p = the new (reduced) price of an orange and (q + 4) = the new number of oranges that can be purchased at the reduced price. Our new equation for total cost is:

(0.6p)(q + 4) = 12

0.6pq + 2.4p = 12

Substituting for q, we have:

0.6p(12/p) + 2.4p = 12

7.2 + 2.4p = 12

2.4p = 4.8

p = 2

That is, each orange is $2. So for $24, we can buy 24/2 = 12 oranges.

Answer: B

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