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mspeople
let's say the smallest number is x, then the largest number is 10+x. Now we can let y be the factor that we multiply the ratio by to get the original numbers. So we have xy=2 and 10y+xy=4. Subtracting the 1st equation from the 2nd we get 10y=2 so y=1/5 which means x=10 and 10+x=20 so the middle number is 15.

Answer:  The required middle number is 15.

Step-by-step explanation:  Given that the ratio of three numbers is 2 : 3 : 4. The largest number is 10 more than the smallest.

We are to find the middle number.

Let 2x, 3x and 4x represents the three numbers.

Then, according to the given information, we have

[tex]2x+10=4x\\\\\Rightarrow 4x-2x=10\\\\\Rightarrow 2x=10\\\\\Rightarrow x=\dfrac{10}{2}\\\\\Rightarrow x=5.[/tex]

Therefore, the middle number is given by

[tex]3\times5=15.[/tex]

Thus, the required middle number is 15.

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