In a photo studio, 200 people were employed. 1/4 of them were men, 1/2 of the remainder were women and the rest were children. How many children were employed? 2. There were 280 people attending a con

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FRIDAY

1. In a photo studio, 200 people were employed. $\frac{1}{4}$ of them were men, $\frac{1}{2}$ of the remainder were women and the rest were children. How many children were employed?

Step 1: Calculate the number of men.
Number of men $= \frac{1}{4} \times 200 = 50$ men.

Step 2: Calculate the remainder after men.
Remainder $= 200 - 50 = 150$ people.

Step 3: Calculate the number of women.
Number of women $= \frac{1}{2} \times 150 = 75$ women.

Step 4: Calculate the number of children.
Number of children $= \text{Remainder} - \text{Number of women}$
Number of children $= 150 - 75 = 75$ children.
There were $\boxed{75}$ children employed.

2. There were 280 people attending a conference. The ratio of men and women was 3:4. Later, 20 men and 40 women left the conference. What was the ratio of men to women who remained?

Step 1: Calculate the initial number of men and women.
Total ratio parts $= 3 + 4 = 7$.
Value of one ratio part $= \frac{280}{7} = 40$.
Initial number of men $= 3 \times 40 = 120$ men.
Initial number of women $= 4 \times 40 = 160$ women.

Step 2: Calculate the number of men and women who remained.
Men remaining $= 120 - 20 = 100$ men.
Women remaining $= 160 - 40 = 120$ women.

Step 3: Express the new ratio of men to women and simplify it.
New ratio $= 100 : 120$.
Divide both sides by their greatest common divisor, which is 20.

$$\frac{100}{20} : \frac{120}{20} = 5 : 6$$

The ratio of men to women who remained was $\boxed{5:6}$.

3. Simplify the following ratios: