Question

If three times the larger of two numbers is divided by the smaller, the quotient is 6 and the remainder is 6. If five times the smaller is divided by the larger the quotient is 2 and the remainder is 3. Find the numbers.

Answer 1

Answer:

16/9 and -1/9

Step-by-step explanation:

let smaller number = x

greater number = y

According to question,

3y / x then 6 is quotient and 6 is remainder

3y = 6x + 6

3y - 6x = 6

y - 2x = 2 ......... (i)

5x / y quotient is 2 and remainder is 3

5x = 2y + 3

2y - 5x = -3 .........(ii)

for making y = 2y multiply by 2 in (i)

2y - 4x = 4 ......(iii)

subtract (ii) from (iii)

-9x = 1

x = -1/9

putting value of x in (i)

y -(-2/9) = 2

y + 2/9 = 2

y = 2-2/9

y = 16/9