SOLUTION: I told a fruit seller to give me Rs. 1680 worth of passion fruits. After he gave me the passion fruits, I forced him to give me 4 extra passion fruits for free. He complained that

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Question 1198564: I told a fruit seller to give me Rs. 1680 worth of passion fruits. After he gave me the passion fruits, I forced him to give me 4 extra passion fruits for free. He complained that because of giving me the extra passion fruits, he is getting Rs. 120 per dozen less on this transaction than the original price. How many passion fruits did get (including the 4 extra passion fruits)?
Found 5 solutions by Theo, ikleyn, greenestamps, MathTherapy, josgarithmetic:
Answer by Theo(13342)   (Show Source):
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x is the number of passion fruit.
p is the price for each passion fruit.

your first eqution is x * p = 1680.

when he gets 4 more passion fruits for free, the price per dozen pawsion fruit becomes less by 120 per dozen.
120 / 12 = less by 10 per passion fruit.

your second equation is (x + 4) * (p - 10) = 1680

simplify that eqution to get xp - 10x + 4p - 40 = 1680
subtract 1680 from both sides of the equation to get xp - 10x + 4p - 1720 = 0

from the first equation, solve for p to get p = 1680/x
replace p in the second equation with 1680/x to get:
x * 1680/x - 10x + 4 * 1680/x - 1720 = 0
simplify to get:
1680 - 10x + 6720/x - 1720 = 0
multiply both sides of that equation by x to get:
1680x - 10x^2 + 6720 - 1720x = 0
combine like terms and reorder the equation in descending order of degree to get:
-10x^2 - 40x + 6720 = 0
multiply both sides of this equation by -1 to get:
10x^2 + 40x - 6720 = 0
divide both sides of this equation by 10 to get:
x^2 + 4x - 672 = 0
factor this quadratic equation to get:
x = -28 or x = 24
since x can't be negative, then x = 24 looks like it's your solution.
in the first equation, replace x with 24 to get 24p = 1680
solve for p to get p = 70.
in your second equation, replace x with 24 to get 28 * p = 1680
solve for p to get p = 60.

the requirements of the problem are satisfied.
when he receives 24 passion fruits, the price is 70 for each passion fruit.
when he receives 4 extra passion fruits for free, he gets 28 passion fruits for the same cost of 1680.
the price per passion fruit becomes 60.

your solution is that he got 28 passion fruits, including the 4 that he got for free.

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

This wording in your post is more appropriate for a police report,
investigating a crime, than for a Math problem.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Let n be the original number of passion fruits.

Before the additional 4 passion fruits were given, the cost per fruit was Rs. 1680/n.

Afterwards, the cost per fruit was Rs. 1680/(n+4).

The decrease in cost was Rs. 120 per dozen, or Rs. 10 per fruit:

Clear fractions by multiplying by the least common denominator, n(n+4):

or

The negative answer makes no sense, so the original number of passion fruits was n=24.

With the additional 4 passion fruits, the total he got was 24+4 = 28.

ANSWER: 28

Answer by MathTherapy(10552)   (Show Source):
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I told a fruit seller to give me Rs. 1680 worth of passion fruits. After he gave me the passion fruits, I forced him to give me 4 extra passion fruits for free. He complained that because of giving me the extra passion fruits, he is getting Rs. 120 per dozen less on this transaction than the original price. How many passion fruits did get (including the 4 extra passion fruits)?

As he received fruits for Rs. 120 LESS than regular price, per dozen, he rec’d EACH fruit for , or Rs. 10. We then get: Regular price per fruit - Discounted price per fruit = Rs. 10. Let number of fruits rec’d be r Then total number of fruits seller purchased = r - 4 We then get: ------ Factoring out numerator-GCF, 10 168r - 168(r - 4) = r(r - 4) ------ Multiplying by LCD, r(r - 4) r - 28 = 0 OR r + 24 = 0 Number of fruits rec’d, or r = 28 OR r = - 24 (ignore)

Answer by josgarithmetic(39617)   (Show Source):
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Rs 120 per dozen = Rs 120 per 12 each = Rs 10 each

CONDITIONS PRICE QUANTITY COST Normal 1680/n n 1680 Unfair 1680/(n+4) n+4 1680 Difference 10

The price difference for each passion fruit was Rs 10.

The normal and fair quantity was 24 passion fruit.
Person telling the story achieved 28 passion fruit.