SOLUTION: Karen intends to buy some oranges. At the market price she will need to pay 96.00 for those oranges. The vendor discounted the price by 2.00 each. At the new priceshe was able to b

Question 697818: Karen intends to buy some oranges. At the market price she will need to pay 96.00 for those oranges. The vendor discounted the price by 2.00 each. At the new priceshe was able to buy some 8 more orangespaying the same amount. How many oranges did she buy?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Before the discount the amount she would have paid = n*p,
where n=the number of oranges, p=the original price
After the discount, the amount paid is (n+8)(p-2) [8 more oranges, 2 dollars less]
In both cases, the amount paid is $96:
np = 96 -> p = 96/n
(n+8)(p-2) = 96 -> (n + 8)(96/n - 2) = 96
Performing the arithmetic, we get
n^2 + 8n - 384 = 0
Factor:
(n+24)(n-16) = 0
Take the positive solution, n=16
So she purchases 16+8 = 24 oranges at the new price

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