Fruit Problem

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Fruit Problem

A farmer is selling 515 pieces of fruit for $150.00,
each apple costs 10 cents, each peach costs 50 cents and each pine apple costs 100 cents. find the number of each kind of fruit.

Posted 250 day ago

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Answers (3)

This is a so called Diophantos type problem. These problems usually have several correct answer. But if additional information is added, the solution can be restricted to only one answer.
Here is just one way of starting the solution:
let x be the number of apples
let y be the number of peaches
let z be the number of pineapples. So
x+ y+ z = 515 (1)
and 10x +50 y + 100 z = 15000 cents (2)
Multiplying (1) by 10, we get:
10x + 10 y + 10 z = 5150 (3)
subtracting (3) from (2) we get:
40 y + 90 z = 9850 or:
4y + 9z = 985.(4). Using congruence, we write:
4y + 9z == 985(mod 4)
but 4 == 0 (mod4), so
0y + 9z == 985 (mod 4)
z = (985 - 4t)/9. for t= 55, we get:
z = 765/9 = 85. inserting in (4), we get:
y=55, and from (1) we get x=375.
Check: 375x10 + 55x50+ 85x100 = 15000 cents or
$150.00.
Also: 85+55+375 = 515.
Of course, as I said other solutions are possible unless we add some restrictions.

Posted 250 day ago

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math_fanatic

This is very similar to the question you posted yesterday. Yesterday you provided 3 variables and one equation and today you provided 3 variables and 2 equations. You must have the same number of equations as variables in order to solve for them.

There may be more than one solution to this problem but I can't find any of them without a lot of guesswork and that's not what algebra is about.

Are you making up these problems or getting them out of a book?
If you made it up yourself, you need to provide more information such as "there are twice as many apples as there are peaches" or "there are 3 more peaches than there are apples". Otherwise this problem is practically impossible to solve.

Posted 250 day ago

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MFB13

The number of apples = 400
The number of peaches = 10
The number of pineapples = 105

Posted 250 day ago

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Question Title	Fruit Problem
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