Question

what number should be added to each of the numbers 8,15,18,30, such that resulting number are in propotition​

Answer 1

SOLUTION

TO DETERMINE

The number should be added to each of the numbers 8,15,18,30, such that resulting number are in proportion

EVALUATION

Let x be the required number

So by the given condition

$\displaystyle \sf{(8 + x) : (15 + x) = (18 + x) : (30 + x)}$

$\displaystyle \sf{ \implies \: \frac{8 + x}{15 + x} = \frac{18 + x}{30 + x} }$

$\displaystyle \sf{ \implies \: 240 + 8x + 30x + {x}^{2} = 270 + 15x + 18x + {x}^{2} }$

$\displaystyle \sf{ \implies \: 5x = 30 }$

$\displaystyle \sf{ \implies \: x = 6 }$

So the required number is 6 so that the resulting numbers 14, 21, 24, 36 are in proportion

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