Question

*If 460 is divided by a natural number, the quotient is 6 more than five times the divisor and the remainder is 1. Write an equation of the given information.*

1️⃣ 5x² + 6x − 460 = 0
2️⃣ 5x² + 6x + 461 = 0
3️⃣ 5x² + 6x −459 = 0
4️⃣ 5x² + 6x + 460 = 0​

Answer 1

According to the question -

If 460 is divided by a natural number.

• Let the number (divisor) be x.

the quotient is 6 more than five times the divisor.

• Here, quotient will be (5x + 6).

and the remainder is 1.

We have :

• Divisor = x

• Quotient = 5x + 6

• Dividend = 460

• Remainder = 1

We know that :

Dividend = Divisor × Quotient + Remainder

Putting the values...

460 = x × (5x + 6) + 1

460 = 5x² + 6x + 1

5x + 6x + 1 - 460 = 0

5x + 6x - 459 = 0

Hence, Option 3 is correct !