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​

Answer 1

Step-by-step explanation:

let the divisor be 'x'

the the quotient is (6+5x)

we know that

divident = divisor ×quotient +remainder

460=x(6+5x)+1

460=6x+5x²+1

460=5x²+6x+1

5x²+6x+1-460=0

5x²+6x-459=0

5x²-45x+51x-459=0

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

(5x+51)(x-9)0

5x+51=0 or x-9=0

5x=-51 or x=9

x=-51/5 or x=9

but -51/5 is not a natural number

thus x= 9

remainder=9

quotient = 5x+6=5(9)+6=45+6=51

the quotient is 51 and the remainder is 9

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Answer 2

Answer:

If 460 is divided by a natural number quotient is 6 more than five times the divisor and remainder is 1, the quotient and divisor​ are 51 and 9 respectively.

Step-by-step explanation:

Let the natural number be x.

Since we have a remainder of 1, the quotient is given by:

(460 - 1)/x = quotient

Now, the quotient is 6 more than 5 times the divisor. So, we have:

quotient = 5x + 6

Substituting this in the first equation we have:

(460 - 1)/x = 5x + 6

459/x = 5x + 6

459 = 5x² + 6x

We get a quadratic equation.

Solving it we have:

5x² + 6x - 459 = 0

Applying the quadratic formula we have:

x = [-6±√(6² + 4 × 459 × 5)]/(2 × 5)

x = [-6±96]/10

x = 9 or -10.20

We take 9 since it's a natural number.

So, the divisor in this case is 9.

The quotient = 5 × 9 + 6 = 51