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Answer :
To solve the problem, "14.2 is 35.5% of what number [tex]\( w \)[/tex]?", we need to find the original number this percentage is calculated from.
Here are the steps to solve the problem:
1. Understand the Relationship: The statement "14.2 is 35.5% of a number [tex]\( w \)[/tex]" implies that 35.5% of [tex]\( w \)[/tex] equals 14.2. In mathematical terms, this is represented as:
[tex]\[
14.2 = 35.5\% \times w
\][/tex]
2. Convert the Percentage to a Decimal: The percentage 35.5% needs to be converted into a decimal to use in the equation. To convert a percentage to a decimal, divide by 100:
[tex]\[
35.5\% = \frac{35.5}{100} = 0.355
\][/tex]
3. Set Up the Equation: Now, substitute the decimal form of 35.5% into the equation:
[tex]\[
14.2 = 0.355 \times w
\][/tex]
4. Solve for [tex]\( w \)[/tex]: To find [tex]\( w \)[/tex], divide both sides of the equation by 0.355:
[tex]\[
w = \frac{14.2}{0.355}
\][/tex]
5. Calculate the Result: When you perform the division:
[tex]\[
w = 40.0
\][/tex]
Thus, the number [tex]\( w \)[/tex] is 40.0. Therefore, 14.2 is 35.5% of 40.0.
Here are the steps to solve the problem:
1. Understand the Relationship: The statement "14.2 is 35.5% of a number [tex]\( w \)[/tex]" implies that 35.5% of [tex]\( w \)[/tex] equals 14.2. In mathematical terms, this is represented as:
[tex]\[
14.2 = 35.5\% \times w
\][/tex]
2. Convert the Percentage to a Decimal: The percentage 35.5% needs to be converted into a decimal to use in the equation. To convert a percentage to a decimal, divide by 100:
[tex]\[
35.5\% = \frac{35.5}{100} = 0.355
\][/tex]
3. Set Up the Equation: Now, substitute the decimal form of 35.5% into the equation:
[tex]\[
14.2 = 0.355 \times w
\][/tex]
4. Solve for [tex]\( w \)[/tex]: To find [tex]\( w \)[/tex], divide both sides of the equation by 0.355:
[tex]\[
w = \frac{14.2}{0.355}
\][/tex]
5. Calculate the Result: When you perform the division:
[tex]\[
w = 40.0
\][/tex]
Thus, the number [tex]\( w \)[/tex] is 40.0. Therefore, 14.2 is 35.5% of 40.0.
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