Step 1: Understanding the Problem
The problem can be rewritten as "What percentage of 112 is 95.75?" This is essentially a question of finding a fraction of 112 that equals 95.75. To approach this, one needs to understand the concept of percentage and proportion. Percentage is a way of expressing a value as a fraction of 100, while proportion is a statement of equality between two ratios.For example, if we know that 25% of 112 is equal to 28, then we can set up an equation to represent this relationship. The equation would be: 0.25 x 112 = 28. This shows that 25% of 112 is equal to 28.
Step 2: Converting Percentages to Decimals
For example, to convert 95.75% to a decimal, we would divide 95.75 by 100. This gives us 0.9575.
Step 3: Setting Up the Proportion
Now that we have the decimal representation of the percentage, we can set up a proportion to solve the problem. The proportion will be in the form of "part/whole = percentage/decent". We will use the decimal representation of the percentage and the given value of 112.Using the same example as before, we can set up the proportion as: 95.75 / 112 = 0.9575 / 1. This shows that 95.75 is equal to 95.75% of 112.
Step 4: Solving the Proportion
To solve the proportion, we need to isolate the percentage. This can be done by cross-multiplying and then dividing by the whole value.| Step | Equation | Result |
|---|---|---|
| 1 | 95.75 x 1 = 95.75 x 0.9575 | 91.625 |
| 2 | 112 / 0.9575 = 117.318 | 117.318 |
By solving the proportion, we have found that 95.75% of 112 is equal to approximately 91.63.
Step 5: Calculating the Percentage
Finally, we can calculate the percentage by dividing the value by the whole value and multiplying by 100.Using the same example as before, we can calculate the percentage as: (91.63 / 112) x 100 = 82.00%. This shows that 95.75 is equal to approximately 82.00% of 112.
Real-World Applications
The problem of "95.75 is what percent of 112" has many real-world applications. One common example is when calculating sales tax or tips. If a customer orders a meal for $112 and wants to leave a 95.75% tip, then we can use the above method to calculate the tip amount.- First, we need to convert the percentage to a decimal: 95.75 / 100 = 0.9575.
- Next, we can set up a proportion to solve for the tip amount: 95.75 / 112 = 0.9575 / 1.
- Then, we can cross-multiply and divide by the whole value to solve for the tip amount.
- Finally, we can calculate the tip amount by multiplying the tip amount by 100.
Common Mistakes to Avoid
There are several common mistakes to avoid when solving the problem of "95.75 is what percent of 112".- One common mistake is to confuse the percentage with the decimal representation. For example, if we know that 95.75 is equal to 95.75% of 112, then we should not confuse this with the decimal representation of 95.75, which is 0.9575.
- Another common mistake is to solve the proportion incorrectly. For example, if we set up the proportion as 95.75 / 112 = 0.9575 / 1, then we should not forget to cross-multiply and divide by the whole value.