A number is divided into two parts such that one part is 10 more than ...
Problem Statement:
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 5:4, find the number and the two parts.
Solution:
Let the number be x.
Step 1: Set up Equations
According to the problem, the two parts are in the ratio 5:4. Therefore, let one part be 5y and the other part be 4y.
Given that one part is 10 more than the other, we can set up the equation:
5y = 4y + 10
Step 2: Solve the Equation
Solving the equation, we get:
y = 10
Step 3: Find the Number and the Two Parts
Now, substitute the value of y back into the parts:
One part = 5y = 5 * 10 = 50
The other part = 4y = 4 * 10 = 40
Therefore, the number is the sum of the two parts: 50 + 40 = 90
Conclusion:
The number is 90, and the two parts are 50 and 40.