There are two distinct natural numbers. Each is first increased by 10 then by same percentage as each was increased for the first time. Each number finally results in 72 Find the difference between the numbers.
How to solve in easy way please help me
Oh, it's a math problem! Let me put on my thinking clown nose for this one. 🤡
Let's call the two distinct natural numbers x and y. According to the problem, each number is first increased by 10 and then increased by the same percentage as it was increased the first time.
So, we can set up two equations based on the given information:
x + 10 + (x + 10) * p = 72 (Equation 1)
y + 10 + (y + 10) * p = 72 (Equation 2)
Here, p represents the percentage increase. Now, we can solve these equations to find x and y.
First, let's simplify Equation 1:
2x + 20p + 10 = 72
Now, let's simplify Equation 2:
2y + 20p + 10 = 72
We can ignore the 10 since it appears on both sides. So now, we have:
2x + 20p = 62 (Equation 1 simplified)
2y + 20p = 62 (Equation 2 simplified)
From these two equations, we can see that 2x + 20p is equal to 2y + 20p. The 20p terms cancel out. So:
2x = 2y Divide both sides by 2.
x = y
Hence, the difference between the two numbers x and y is 0. They are the same number!
I hope my math clowning brought a smile to your face! Let me know if you need any more assistance. 🤡
Let's denote the two distinct natural numbers as x and y.
Step 1: Increase each number by 10:
x + 10 and y + 10
Step 2: Increase each number by the same percentage as the first increase:
(x + 10) + ((x + 10) * p) and (y + 10) + ((y + 10) * p)
Step 3: Each number finally results in 72:
(x + 10) + ((x + 10) * p) = 72
(y + 10) + ((y + 10) * p) = 72
Step 4: Solve the system of equations:
By rearranging the equation in Step 3, we get:
(x + 10) * (1 + p) = 72
(y + 10) * (1 + p) = 72
Divide both sides of the equations by (1 + p):
x + 10 = 72 / (1 + p)
y + 10 = 72 / (1 + p)
Subtract 10 from both sides of the equations:
x = 72 / (1 + p) - 10
y = 72 / (1 + p) - 10
Step 5: Find the difference between the numbers (x - y):
(x - y) = (72 / (1 + p) - 10) - (72 / (1 + p) - 10)
Simplifying the equation, we get:
(x - y) = 72 / (1 + p) - 72 / (1 + p)
The numerator in both fractions is the same, so the difference is 0.
Therefore, the difference between the two numbers is 0.
To solve this problem, we can break it down into steps:
Step 1: Assign variables
Let's assign variables to represent the two distinct natural numbers. We will call them "x" and "y".
Step 2: Set up equations
Based on the problem statement, we know that each number is first increased by 10, and then by the same percentage as the first increase. This can be represented as follows:
For the first number:
x + 10 + (10% of x) = 72
For the second number:
y + 10 + (10% of y) = 72
Step 3: Solve the equations
To solve the equations, we substitute the value of x from the first equation into the second equation. This yields:
y + 10 + (10% of y) = 72
Simplifying further, we have:
1.1y + 10 = 72
Subtracting 10 from both sides of the equation:
1.1y = 62
Dividing both sides by 1.1:
y = 56.36
Step 4: Find the difference between the numbers
Now that we have the value of y, we can substitute it back into the first equation to find the value of x:
x + 10 + (10% of x) = 72
x + 10 + (0.1x) = 72
1.1x + 10 = 72
Subtracting 10 from both sides:
1.1x = 62
Dividing both sides by 1.1:
x = 56.36
The difference between the two numbers is the absolute difference between their values:
|y - x| = |56.36 - 56.36| = 0
Therefore, the difference between the numbers is 0.