Question

If 280 is divided by a natural number, then the quotient is 3 more than twice the divisor and the remainder is 5. Find the quotient and the divisor.

Answer 1

Answer:

Step-by-step explanation:

Let the Divisor be X.

Then the Quotient = 2X+3

Dividend = 280

Remainder = 5

We know that,

Dividend = Divisor × Quotient + Remainder

280 = X × (2X+3) + 5

280 = 2X²+3X+5

2X²+3X-275 = 0

2X²+25X-22X-275 = 0

X(2X+25)-11(2X+25) = 0

(X-11) (2X+25)= 0

(X-11)= 0 OR(2X+25) = 0

(X-11) = 0

X = 11

Divisor = X = 11

And,

Quotient = 2X +3 = 2 × 11 + 3 = 25.