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Math  /  Numbers & Operations

QuestionDecimals, Proportions, and Percents Applying the percent equation: Problem type 1 nswer the following questions. (a) What number is 15%15 \% of 80 ? (b) 45%45 \% of what is 18?18 ?

Studdy Solution

STEP 1

1. We are dealing with percentages and their applications in finding parts of a whole.
2. For part (a), we need to find what number is 15% 15\% of 80 80 .
3. For part (b), we need to find the whole when 45% 45\% of it is 18 18 .

STEP 2

1. Solve part (a) using the percent equation.
2. Solve part (b) using the percent equation.

STEP 3

For part (a), we need to find 15% 15\% of 80 80 . The percent equation is:
Part=(Percent100)×Whole \text{Part} = \left(\frac{\text{Percent}}{100}\right) \times \text{Whole}

STEP 4

Substitute the given values into the equation:
Part=(15100)×80 \text{Part} = \left(\frac{15}{100}\right) \times 80

STEP 5

Calculate the part:
Part=0.15×80=12 \text{Part} = 0.15 \times 80 = 12

STEP 6

For part (b), we need to find the whole when 45% 45\% of it is 18 18 . The percent equation is:
Part=(Percent100)×Whole \text{Part} = \left(\frac{\text{Percent}}{100}\right) \times \text{Whole}

STEP 7

Rearrange the equation to solve for the whole:
Whole=Part(Percent100) \text{Whole} = \frac{\text{Part}}{\left(\frac{\text{Percent}}{100}\right)}

STEP 8

Substitute the given values into the equation:
Whole=18(45100) \text{Whole} = \frac{18}{\left(\frac{45}{100}\right)}

STEP 9

Calculate the whole:
Whole=180.45=40 \text{Whole} = \frac{18}{0.45} = 40
The solutions are: (a) 15% 15\% of 80 80 is 12 \boxed{12} . (b) 45% 45\% of 40 \boxed{40} is 18 18 .

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