Question

The difference between two natural numbers is 39. If the larger number is divided by the smaller one, then the quotient is 3 and the remainder is 11. The smaller number =

Answer 1

-------------------------------------------
Define x and y :
-------------------------------------------
Let one number be x and the other number will be x + 39

-------------------------------------------
Construct equation :
-------------------------------------------
When the big number divided by the smaller number, the quotient is 3 with 11 remaining
⇒
`(x + 39 - 11)/(x) = 3`

-------------------------------------------
Solve x :
-------------------------------------------

`(x + 39 - 11)/(x) = 3`


`(x + 28)/(x) = 3`


`x + 28 = 3x`


`2x = 28`


`x = 14`

-----------------------------
Find the numbers:
-----------------------------
small number = x = 14

big number = x + 39 = 14 + 39 = 53

-------------------------------------------
Answer: The smaller number is 14.
-------------------------------------------