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Math  /  Algebra

QuestionChallenge In a company, 75%75 \% of the workers are women. If 525 people work for the company who aren't women, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
There are □\square workers in all. (Type a whole number.)

Studdy Solution

STEP 1

1. 75% of the workers are women.
2. 525 people are not women.
3. We need to find the total number of workers in the company.

STEP 2

1. Method 1: Use percentage complement.
2. Method 2: Use algebraic equation.
**Method 1: Use percentage complement**

STEP 3

Identify the percentage of workers who are not women. Since 75% of the workers are women, the remaining percentage of workers who are not women is:
100%−75%=25% 100\% - 75\% = 25\%

STEP 4

Use the percentage of non-women workers to find the total number of workers. Let x x be the total number of workers. Since 25% of the workers are not women, we can write:
0.25×x=525 0.25 \times x = 525

STEP 5

Solve for x x by dividing both sides of the equation by 0.25:
x=5250.25 x = \frac{525}{0.25}
Calculate the division:
x=2100 x = 2100
**Method 2: Use algebraic equation**

STEP 6

Define the total number of workers as x x . Since 75% of the workers are women, 25% are not women. Therefore, the number of workers who are not women is:
0.25×x=525 0.25 \times x = 525

STEP 7

Solve for x x by dividing both sides of the equation by 0.25:
x=5250.25 x = \frac{525}{0.25}
Calculate the division:
x=2100 x = 2100
The total number of workers in the company is:
2100 \boxed{2100}

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