Adding 15 percent of x to x is equivalent to multiplying x by
The Correct Answer and Explanation is:
Correct Answer:
Adding 15 percent of xx to xx is equivalent to multiplying xx by 1.15.
Explanation
To understand why adding 15 percent of a number xx to itself is the same as multiplying it by 1.15, we need to break it down step by step using basic algebra and percentages.
Step 1: Understanding 15 percent of xx:
Percent means “per hundred,” so 15% of xx is written mathematically as: 15% of x=15100×x=0.15×15\% \text{ of } x = \frac{15}{100} \times x = 0.15x
Step 2: Adding 15% of xx to xx:
This means taking the original xx, and adding 0.15 times xx to it: x+0.15xx + 0.15x
Because both terms contain xx, you can factor it out: x+0.15x=(1+0.15)x=1.15xx + 0.15x = (1 + 0.15)x = 1.15x
So the result of adding 15% of xx to xx is 1.15×1.15x, which is the same as multiplying xx by 1.15.
Real-Life Example:
Let’s say x=100x = 100.
15% of 100 is: 0.15×100=150.15 \times 100 = 15
Adding this to 100 gives: 100+15=115100 + 15 = 115
Alternatively, multiplying 100 by 1.15: 1.15×100=1151.15 \times 100 = 115
Both methods give the same result. This shows clearly that adding 15% to a number is the same as multiplying it by 1.15.
Conclusion:
This principle applies to any percentage increase. For example, adding 20% is multiplying by 1.20; adding 50% is multiplying by 1.50, and so on. So, adding 15 percent of xx to xx is equivalent to multiplying xx by 1.15.
