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.
starting value: x
increase by 10: x+10
increase by percent increase:
x+10 + 10/x
result is 72:
x+10 + 10/x = 72
x = 31±√951
difference between the two values: 2√951
But those are not natural numbers. So, what do I have wrong?
To find the difference between the two numbers, we'll need to solve this problem step by step.
Let's assume the two distinct natural numbers as x and y.
According to the problem, each number is first increased by 10, so the new values become x + 10 and y + 10, respectively.
Next, each number is increased by the same percentage as they were for the first time. Let's assume the increase percentage as p%.
Therefore, the new values after the second increase become (x + 10) * (1 + p/100) and (y + 10) * (1 + p/100), respectively.
Finally, we know that both of these new numbers result in 72. So, we can set up the following equations:
(x + 10) * (1 + p/100) = 72 ---- (1)
(y + 10) * (1 + p/100) = 72 ---- (2)
Now, let's solve these equations to find the values of x, y, and p.
From equation (1):
(x + 10) * (1 + p/100) = 72
Expanding the equation:
x + 10 + (p/100)*x + (p/100)*10 = 72
Bringing like terms together:
x + 10 + (p/100)*(x + 10) = 72
Factoring out x + 10:
(x + 10)(1 + p/100) = 72
Dividing both sides by (1 + p/100):
x + 10 = 72 / (1 + p/100)
x + 10 = 72 * (100 / (100 + p))
Similarly, from equation (2):
(y + 10) * (1 + p/100) = 72
Expanding it and factoring out y + 10, we get:
(y + 10) = 72 / (1 + p/100)
y + 10 = 72 * (100 / (100 + p))
Now that we have the expressions for x and y, let's find their difference:
Difference = (x + 10) - (y + 10)
= x - y
To find the value of x - y, we need to know the value of p. However, the problem doesn't provide any information about the actual value of p. Therefore, we cannot determine the exact difference between the numbers without knowing the value of p.