A number is divided into two parts such that one part is 10 more than the
other. If the two parts are in the ratio 5:3. Find the number and the two
parts
let the two parts be 5x and 3x
"one part is 10 more than the
other"
---> 5x = 3x+10
2x=10
x = 5
the two parts are 25 and 15, and the whole number was 40
10
To solve this problem, let's break it down step by step:
Let's assume that the number is represented by 'x'. We are told that one part is 10 more than the other.
So, the two parts can be represented as (x - 10) and (x + 10).
We are also given that these two parts are in the ratio 5:3.
In mathematical terms, this can be written as:
(x - 10) / (x + 10) = 5/3
To solve this equation, we can cross-multiply:
3*(x - 10) = 5*(x + 10)
Expanding both sides of the equation, we get:
3x - 30 = 5x + 50
Bringing the x terms to one side and the constants to the other side, we have:
3x - 5x = 50 + 30
-2x = 80
Dividing both sides of the equation by -2, we get:
x = -40
Therefore, the number is -40.
The two parts can be found by substituting this value of x in the expressions we derived earlier:
One part = (x - 10) = (-40 - 10) = -50
Other part = (x + 10) = (-40 + 10) = -30
So, the two parts are -50 and -30, respectively.