Math, asked by snjothi08, 1 year ago

A number is 42 more than the average of its half ,one third and one fifteen .Find the numbers.

Answers

Answered by Kmg13teen

Let the number be x

thus from given condition

$average = \frac{x}{2} + \frac{x}{3} + \frac{x}{15} \\ \\ = \frac{15x}{30} + \frac{10x}{30} + \frac{2x}{30} \\ \\ = \frac{27x}{30} = \frac{9x}{10} \\ \\ = \frac{ \frac{9x}{10} }{3} \\ \\ = \frac{9x}{10} \times \frac{1}{3} \\ \\ = \frac{3x}{10} \: is \: the \: average$
But from the given condition

$x = 42 + \frac{3x}{10} \\ \\ x = \frac{420 + 3x}{10} \\ \\ 10x = 420 + 3x \\ 10x - 3x = 420 \\ \\ 7x = 420 \\ \\ x = 60$
The number is 60

snjothi08: i can't understand

Kmg13teen: we know that average is equal to sum of observations divided by number of observations or average = sum of observations/ no. of observations

Kmg13teen: then considering the number as x, and finding the average of its half i.e x/2 , its one third i.e x/3 and its one fifteenth i.e. x/15

Kmg13teen: thus adding these fractions (I hope you know how to add fractions) and dividing them by 2

Kmg13teen: sorry dividing them by 3 since there are three terms

Kmg13teen: after all those calculations we got

Kmg13teen: 3x/10 as average. But it's given that the number is 42 more than that average

Kmg13teen: thus writing it as equation we get

Kmg13teen: i.e. that number(x)= 42 + 3x/10(average of the given terms)

Kmg13teen: Hope you understood

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