To divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part, we can use algebraic equations to solve for the two parts.

Let's assume the first part is represented by "x" and the second part is represented by "y".

1. Define the Variables:
Let x be the first part and y be the second part.

2. Set up the Equations:
According to the problem, 5% of the first part is equal to 10% of the second part. Mathematically, this can be written as:
0.05x = 0.10y

3. Convert Percentages to Decimals:
To make the equation easier to work with, we convert the percentages to decimals by dividing by 100:
0.05x = 0.10y can be simplified to 0.05x = 0.01y

4. Set up the Second Equation:
We also know that the sum of the two parts is equal to 4500. Mathematically, this can be written as:
x + y = 4500

5. Solve the System of Equations:
Now we have a system of two equations:
0.05x = 0.01y (Equation 1)
x + y = 4500 (Equation 2)

To solve this system, we can use substitution or elimination method.

a. Substitution Method:
From Equation 2, we can solve for x:
x = 4500 - y

Now we substitute this value of x into Equation 1:
0.05(4500 - y) = 0.01y
225 - 0.05y = 0.01y
225 = 0.06y
y = 225/0.06
y = 3750

b. Elimination Method:
Multiply Equation 1 by 100 to get rid of decimals:
5x = y

Now we can substitute this value of y into Equation 2:
x + 5x = 4500
6x = 4500
x = 4500/6
x = 750

6. Verify the Solution:
Now we have the values for x and y:
x = 750
y = 3750

To verify, we can check if 5% of the first part is equal to 10% of the second part:
5% of 750 = (5/100) * 750 = 37.5
10% of 3750 = (10/100) * 3750 = 37.5

Therefore, the two parts of 4500 that satisfy the given condition are:
First part (x) = 750
Second part (y) = 3750

Suppose x and y are two divided

parts of 4500. then

x+y=4500 __ (1)

given

5% of x = 10% of y

1005x​=10010y​

x=2y

2y+y=4500

3y=4500

y=1500

x+1500=4500

x=4500−1500

x=3000

hence the 4500 is been divided into 

two parts of 1500 and 3000.



please upvote my answer.
thankyou