calculate the following question:a. 42 is 30% of what number?
The correct answer and explanation is:
Correct Answer: 140
Explanation (300 words):
To solve the question “42 is 30% of what number?”, we need to understand what this sentence is asking in mathematical terms.
Let’s break it down:
- “42 is 30% of what number?” means we are looking for a number such that 30% of it equals 42.
- Let the unknown number be x.
- We write this as an equation: 30% of x=4230\% \text{ of } x = 42 In math, 30% can be written as a decimal: 30%=30100=0.3030\% = \frac{30}{100} = 0.30 So the equation becomes: 0.30⋅x=420.30 \cdot x = 42
Step-by-Step Solution:
- Start with the equation: 0.30x=420.30x = 42
- To find x, divide both sides of the equation by 0.30: x=420.30x = \frac{42}{0.30}
- Perform the division: x=140x = 140
So, the number we are looking for is 140.
Why This Works:
This type of problem involves working backward from a known percentage and result to find the original or whole amount. In percentage problems:
- “is” means equals
- “of” means multiply
- “what number” means the unknown variable (usually x)
Therefore, the phrase “42 is 30% of what number” translates mathematically to: 42=30%×x42 = 30\% \times x
And by solving that, we get the original number, which is 140.