Questions: (a) 25% of what number is 17? (b) 45% of 80 is what?

Transcript text: (a) $25 \%$ of what number is 17 ? (b) $45 \%$ of 80 is what?

Solution

Solution Steps

To solve these percentage problems, we need to use the formula for finding percentages: $ \text{part} = \text{percentage} \times \text{whole} $. For question (a), we need to find the whole when given the part and the percentage. For question (b), we need to find the part when given the whole and the percentage.

Step 1: Solve for the Whole in Question (a)

We need to find the number $ x $ such that $ 25\% $ of $ x $ equals $ 17 $. This can be expressed mathematically as: \[ 0.25x = 17 \] To find $ x $, we rearrange the equation: \[ x = \frac{17}{0.25} = 68.0 \]

Step 2: Solve for the Part in Question (b)

Next, we need to find $ y $ such that $ 45\% $ of $ 80 $ equals $ y $. This can be expressed as: \[ y = 0.45 \times 80 \] Calculating this gives: \[ y = 36.0 \]

Final Answer

For question (a), the number is $ \boxed{68.0} $.
For question (b), $ 45\% $ of $ 80 $ is $ \boxed{36.0} $.

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