Three pieces of fruit have an average weight of m grams. After another piece of fruit is added, the average weight doubles. Find the weight of the extra piece of fruit in terms of m.

x1 = weight of the first piece

x2 = weight of the secound piece

x3 = weight of the third piece

x4 = weight of the fourth piece ( extra piece )

Average weight of first three pieces:

( x1 + x2 + x3 ) / 3 = m

Multiply both sides by 3

x1 + x2 + x3 = 3 m

Average weight of four pieces:

( x1 + x2 + x3 + x4 ) / 4 = 2 m

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Remark:

( x1 + x2 + x3 = 3 m )

so:
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( 3 m + x4 ) / 4 = 2 m

Multiply both sides by 4

3 m + x4 = 8 m

Subtract 3 m to both sides

3 m + x4 - 3 m = 8 m - 3 m

x4 = 5 m

The weight of the extra piece = 5 m

Ah, the perplexing world of fruity averages! Well, let's put our thinking fruit hats on and solve this.

We know that initially, the three fruits had an average weight of m grams. So, if we sum up their weights, we get 3m grams in total.

Now, when we add the fourth fruit, the average weight doubles. This means that the combined weight of the four fruits is now twice the average, which is 2m grams. So, the total weight of the four fruits is 2m grams.

To find the weight of the extra piece of fruit, we can subtract the initial total weight from the new total weight. In other words, we have:

Weight of extra fruit = Total weight of four fruits - Total weight of three fruits

Weight of extra fruit = 2m grams - 3m grams

And if we simplify that, we get:

Weight of extra fruit = -m grams

Oh dear! It seems that the weight of the extra fruit is actually negative in terms of m. That's one wacky fruit indeed! But hey, who am I to judge a fruit by its weight?

Let's assume the weight of the extra piece of fruit is x grams.

We are given that the average weight of three pieces of fruit is m grams. So, the total weight of these three pieces of fruit is 3 * m grams.

When the fourth piece of fruit is added, the average weight doubles. This means that the total weight of all four pieces of fruit becomes 2 * (3 * m + x) grams.

Since the average weight doubles, we can set up the equation:

2(3m + x) = 3m + x + x

Simplifying this equation:

6m + 2x = 3m + 2x

Subtracting 2x from both sides:

6m = 3m

Subtracting 3m from both sides:

3m = 0

Dividing both sides by 3:

m = 0

Since m = 0, we conclude that the weight of the extra piece of fruit, x, is also 0.

Therefore, the weight of the extra piece of fruit in terms of m is 0 grams.

To solve this problem, we can use the concept of averages.

Let's assume the weight of the extra piece of fruit is "x" grams.

The average weight of three pieces of fruit is given as "m" grams. This means that the total weight of the three fruits combined is 3m grams.

When the extra piece of fruit is added, the average weight doubles. So, the average weight becomes 2m grams.

To find the total weight of the four pieces of fruit combined, we can multiply the average weight by the number of fruits: 2m * 4 = 8m grams.

Now, we can set up an equation to find the weight of the extra piece of fruit:
Total weight of 3 fruits + Weight of extra fruit = Total weight of 4 fruits
3m + x = 8m

To solve for "x" in terms of "m", we can rearrange the equation:
x = 8m - 3m
x = 5m

Therefore, the weight of the extra piece of fruit in terms of "m" is 5m grams.