Question

the product of two successive multiples of 5 is 300 ,what are the values of these multiples
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Answer 1

Given :- The product of two successive multiples of 5 is 300. What are the values of these multiples ?

Solution :-

Let us assume that, successive multiples of 5 are 5x and (5x + 5) .

given that ,

→ 5x(5x + 5) = 300

→ 25x² + 25x = 300

→ 25(x² + x) = 300

dividing both sides by 25,

→ x² + x = 12

→ x² + x - 12 = 0

→ x² + 4x - 3x - 12 = 0

→ x(x + 4) - 3(x + 4) = 0

→ (x + 4)(x - 3) = 0

Putting both equal to zero, we get, x is equal to (-4) and 3 .

Therefore,

when x is equal to 3 :-

→ First number = 5x = 5 * 3 = 15 .

→ second number = (5x + 5) = (5*3 + 5) = 15 + 5 = 20.

when x is equal to (-4) :-

→ First number = 5x = 5 * (-4) = (-20) .

→ second number = (5x + 5) = 5*(-4) + 5 = -20 + 5 = (-15).

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Answer 2

SOLUTION :

GIVEN

The product of two successive multiples of 5 is 300

TO DETERMINE

The values of these multiples

CALCULATION

Let the two multiple of 5 be x and x + 5

Then by the given condition

$\sf{}x(x + 5) = 300$

$\implies \sf{} {x}^{2} + 5x - 300 = 0$

$\implies \sf{} {x}^{2} + 20x -15x - 300 = 0$

$\implies \sf{}x(x + 20) - 15(x + 20)= 0$

$\implies \sf{}(x + 20) (x - 15)= 0$

Which gives

$\implies \sf{}either \: (x + 20) = 0 \: \: \: or \: \: \: (x - 15)= 0$

$\sf{}Now \: x + 20 = 0 \: \: gives \: \: x = - 20$

In this case the multiples are - 20 & - 15

$\sf{}Again \: \: x - 15 = 0 \: \: gives \: \: x = 15$

In this case the multiples are 15 & 20

FINAL ANSWER

Hence the required multiples are - 20, - 15 or 15, 20

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