Question
Answer the following questions. \[ \begin{array}{l}\text { (a) } 186 \% \text { of what is } 56.73 \text { ? } \\ \text { (b) What number is } 26.8 \% \text { of } 67.5 ?\end{array} \]
Ask by Schultz Gonzalez. in Qatar
Dec 02,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
(a) 186% of 30.5 is 56.73.
(b) 26.8% of 67.5 is 18.09.
Solution
To solve these problems, we will use the formula for finding a percentage of a number:
\[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]
Let's solve each part separately:
### Part (a):
Given:
- Percentage: 186%
- Part: 56.73
We need to find the Whole.
Using the formula:
\[ \text{Whole} = \frac{\text{Part}}{\text{Percentage}} \times 100 \]
Substitute the given values:
\[ \text{Whole} = \frac{56.73}{186} \times 100 \]
Now, we can calculate the Whole.
### Part (b):
Given:
- Percentage: 26.8%
- Whole: 67.5
We need to find the Part.
Using the formula:
\[ \text{Part} = \frac{\text{Percentage}}{100} \times \text{Whole} \]
Substitute the given values:
\[ \text{Part} = \frac{26.8}{100} \times 67.5 \]
Now, we can calculate the Part.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{56.73}{186}\times 100\)
- step1: Divide the terms:
\(\frac{61}{200}\times 100\)
- step2: Reduce the numbers:
\(\frac{61}{2}\)
Calculate or simplify the expression \( 26.8/100*67.5 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{26.8}{100}\times 67.5\)
- step1: Divide the terms:
\(\frac{67}{250}\times 67.5\)
- step2: Convert the expressions:
\(\frac{67}{250}\times \frac{135}{2}\)
- step3: Multiply the numbers:
\(\frac{1809}{100}\)
### Answers:
(a) 186% of what is 56.73 is 30.5.
(b) 26.8% of 67.5 is 18.09.
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Extra Insights
To find the answers to your questions, let's break them down one by one. (a) To determine "186% of what is 56.73?", we can set up the equation: \[ 186\% \times x = 56.73 \] This can be rephrased as: \[ 1.86x = 56.73 \] Now, divide both sides by 1.86: \[ x = \frac{56.73}{1.86} \approx 30.5 \] So, 186% of approximately 30.5 is 56.73. (b) To find "What number is 26.8% of 67.5?", we can set up the equation: \[ y = 26.8\% \times 67.5 \] Converting the percentage into a decimal, we get: \[ y = 0.268 \times 67.5 \approx 18.09 \] Therefore, 26.8% of 67.5 is approximately 18.09.