Question

a. In a division statement, the quotient is 4 and its remainder is 6.
The sum of the dividend and the divisor is 66. Find the value of
the dividend and the divisor.​

Answer 1

Answer:

Dividend = 54; divisor = 12

Step-by-step explanation:

let the dividend , divisor , quotient and remainder be i , d , q and r respectively.

Dividend = ( divisor × quotient ) + remainder

According to question

i = (d × 4) + 6

i = 4d + 6

4d + 6 = i

4d = i - 6

$d = \frac{i \: - \: 6}{4}$

this will first equation

According to question

i + d = 66

d = 66 - i

this will second equation

From first and second equation

$\frac{i \: - 6}{4} = 66 - \: i$

i - 6 = 4( 66 - i )

i - 6 = 264 - 4i

i + 4i = 264 + 6

i = 270/5

i = 54

if we put value of i in second equation

d = 66 -54

d = 12

hence dividend is equal to 54 and divisor is equal to 12.

Answer 2

Solution:

According to a division rule:

Dividend = Divisor x Quotient + Remainder

Given:
Quotient = 4
Remainder = 6
Sum of dividend and divisor = 66

Let’s say that a = dividend and b = divisor

a = b * 4 + 6

a = 4b + 6

Substitute a to given value to find b.

a + b = 66

4b + 6 + b = 66

5b = 66 - 6

5b = 60

b = 12

Now, solving for a

a + b = 66

a + 12 = 66

a = 66 - 12

a = 54

Therefore, 54/12 = 4 R.6

Hope this will be helpful to you.