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.
Please explain easy way
a+10+10/a=72
a^2+10a-72a+10=0
a^2-62a+10=0
solve quadracticly
How take 10/a can you explain
To find the difference between the two numbers, let's call them x and y. We'll break down the problem step by step:
1. First, increase both numbers by 10: x + 10 and y + 10.
2. Next, increase each of these numbers by the same percentage as the original increase of 10. Let's assume this percentage is P. So, the new numbers become (x + 10) * (1 + P/100) and (y + 10) * (1 + P/100).
3. Finally, we know that both of these numbers result in 72. So, we can set up the following equations:
- (x + 10) * (1 + P/100) = 72
- (y + 10) * (1 + P/100) = 72
To find the difference between the numbers, we need to solve these equations simultaneously.
Here's how you can do it step by step:
1. Expand the equations by distributing the terms:
- (x + 10) + (x + 10) * (P/100) = 72
- (y + 10) + (y + 10) * (P/100) = 72
2. Simplify:
- x + 10 + (x * P/100) + (10 * P/100) = 72
- y + 10 + (y * P/100) + (10 * P/100) = 72
3. Combine like terms:
- x + (x * P/100) + 10 + (10 * P/100) = 72
- y + (y * P/100) + 10 + (10 * P/100) = 72
4. Group the terms:
- (1 + P/100) * x + (1 + P/100) * 10 = 72
- (1 + P/100) * y + (1 + P/100) * 10 = 72
5. Simplify further:
- (1 + P/100) * x + 10 + (10 * P/100) = 72
- (1 + P/100) * y + 10 + (10 * P/100) = 72
6. Subtract 10 from both sides of the equations:
- (1 + P/100) * x = 62 - (10 * P/100)
- (1 + P/100) * y = 62 - (10 * P/100)
7. Divide both sides of the equations by (1 + P/100):
- x = (62 - (10 * P/100)) / (1 + P/100)
- y = (62 - (10 * P/100)) / (1 + P/100)
8. Now we have expressions for x and y in terms of P, the percentage increase. We can use these expressions to find the difference between x and y. Specifically, x - y can be calculated as:
- (62 - (10 * P/100)) / (1 + P/100) - (62 - (10 * P/100)) / (1 + P/100)
To get the numerical value of x - y, you can substitute different values for P and calculate the result. The difference between the two numbers will vary depending on the chosen percentage increase.