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The houses of a row are numbered consecu...

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x (Hint: `S_[x-1]=S_[49]-S_x`)

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To solve the problem, we need to find a value of \( x \) such that the sum of the house numbers before house \( x \) is equal to the sum of the house numbers after house \( x \). ### Step-by-Step Solution: 1. **Understanding the Problem**: We have houses numbered from 1 to 49. We need to find \( x \) such that: \[ S_{x-1} = S_{49} - S_x ...
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Knowledge Check

  • The sum of three numbers is 855. One of the numbers, x, is 50% more than the sum of the other two numbers. What is the value of x ?

    A
    570
    B
    513
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    214
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    155

  • The product of two number x and y is twice the sum of the numbers. What is the sum of the reciprocals of x and y?

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    B
    `1//4`
    C
    `1//2`
    D
    `2`

  • The ratio of the sum of the reciprocal of x and y to the product of the reciprocal of x and y is 1 : 3. What is sum of the numbers x and y?

    A
    `1/3`
    B
    `1/2`
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    `2`

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