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Math  /  Numbers & Operations

QuestionAnswer the following questions. (a) 27 is what percent of 18.75 ? (b) 52.5%52.5 \% of what is 25.83 ?

Studdy Solution

STEP 1

1. For part (a), we need to find what percent 27 is of 18.75.
2. For part (b), we need to find the original number when 52.5% of it equals 25.83.

STEP 2

1. Solve part (a).
2. Solve part (b).

STEP 3

To find what percent 27 is of 18.75, use the formula for percentage:
Percentage=(PartWhole)×100\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100

STEP 4

Substitute the given values into the formula:
Percentage=(2718.75)×100\text{Percentage} = \left(\frac{27}{18.75}\right) \times 100

STEP 5

Calculate the percentage:
Percentage=(2718.75)×100=1.44×100=144%\text{Percentage} = \left(\frac{27}{18.75}\right) \times 100 = 1.44 \times 100 = 144\%

STEP 6

For part (b), use the formula for finding the whole when given a percentage and its part:
Whole=PartPercentage×100\text{Whole} = \frac{\text{Part}}{\text{Percentage}} \times 100

STEP 7

Substitute the given values into the formula:
Whole=25.8352.5×100\text{Whole} = \frac{25.83}{52.5} \times 100

STEP 8

Calculate the original number:
Whole=25.8352.5×100=0.492×100=49.2\text{Whole} = \frac{25.83}{52.5} \times 100 = 0.492 \times 100 = 49.2
The solutions are: (a) 144% 144\% (b) 49.2 49.2

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