Question

If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser. Solve the word problem

Answer 1

Hi ,

Let the natural number = x

according to the problem given ,

460 is divided by x , quotient is 6 more

than five times of x and remainder is 1.

Here ,

dividend = 460

quotient = 5x + 6

divisor = x

remainder = 1

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By Division algorithm :

dividend = divisor × quotient + remainder
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460 = x( 5x + 6 ) + 1

0 = 5x² + 6x - 459

compare 5x² + 6x - 459 = 0 with ax²+bx+c=0

we get

a = 5 , b = 6 , c = -459

discreaminant ( D ) = b² - 4ac

D = 6² - 4 × 5 × ( -459 )

= 36 + 9180

D = 9216

By Quadratic formula :

x = [ ( - b ) ± √D ]/2a

= [ ( -6 )± √9216 ]/( 2 × 5 )

= ( -6 ± 96 )/10

Therefore ,

x = ( -6 + 96 )/10 or x = ( -6 - 96 )/10

x = 90/10 or x = - 102/10

x = 9 or x = - 51/5

But x is a natural number.

Required natural number = x = 9

I hope this helps you.

: )

Answer 2

Hii friend,

Let the Divisor be X.

Then the Quotient = 5X+6

Dividend = 460

Remainder = 1

We know that,

Dividend = Divisor × Quotient + Remainder

460 = X × (5X+6) + 1

460 = 5X²+6X+1

5X²+6X-459 = 0

5X²+51X-45X-459 = 0

X(5X+51)-9(5X+51) = 0

(X-45) (5X+51)= 0

(X-9)= 0 OR(5X-51) = 0

(X-9) = 0

X = 9

Divisor = X = 9

And,

Quotient = 5X +6 = 5 × 9 + 6 = 51.

HOPE IT WILL HELP YOU..... :-)