# Help needed with a Algebra Question

Four apples weigh as much as two melons.Five oranges weigh as much as three melons.Six apples weigh as much as how many oranges ?

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Please, try to make the title of your question more informative. E.g., Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. –  Julian Kuelshammer Oct 30 '12 at 19:01
How many melons weigh as much as six apples? –  Michael Joyce Oct 30 '12 at 19:03

Since $4$ applies weight as much has $2$ melons, $6$ apples will weight as much as $3$ melons. But $5$ oranges weigh as much as $3$ melons. Can you now conclude?

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Thank you for time, appreciate it. I can see the pattern behind it. –  Jay Oct 30 '12 at 19:11

4 apples = 2 melons ---eq.1

5 oranges = 3 melons---eq.2

Multiply equation 1 with 3/2 for making RHS of both the equations same.

Hence,

6 apples= 3 melons---eq.3

Compare eq.2 with eq. 3

Therefore,

6 apples= 5 oranges

Thus 6 apples weigh as much as 5 oranges.

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Thanks a lot, really appreciate your efforts. Simple simultaneous, but I couldn't get my head around it. –  Jay Oct 30 '12 at 19:36

Lets right out what we know in equations.

Let $a =$ weight of apple, $m =$weight of melon, $o =$ weight of orange.

Then we have the following equations: $$4a = 2m$$ $$5o = 3m$$ So we can eliminate $m$ from these equations by multiplying through on the first equation by $\frac{3}{2}$ and subtracting from the first.

So we get $$6a = 3m$$ $$5o = 3m$$ So equating these we get $$6a = 5o$$

Thus we see that $6$ apples weights as much as $5$ oranges.

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Thank you ever so much, really appreciate it. Now I see where I was going wrong. –  Jay Oct 30 '12 at 19:09