To solve the problem of finding out how many women are there at a college where the ratio of men to women is 5 to 4, with 2800 men, follow these steps:
1. Understand the given ratio and quantities:
- The ratio of men to women is 5 to 4.
- There are 2800 men.
2. Represent the ratio mathematically:
- Since the ratio of men to women is 5:4, for every 5 men, there are 4 women.
3. Set up the ratio in equation form:
[tex]\[
\frac{\text{Number of men}}{\text{Number of women}} = \frac{5}{4}
\][/tex]
Let [tex]\( w \)[/tex] represent the number of women.
4. Substitute the known quantity (number of men) into the equation:
[tex]\[
\frac{2800}{w} = \frac{5}{4}
\][/tex]
5. Solve for [tex]\( w \)[/tex] by cross-multiplying:
[tex]\[
2800 \times 4 = 5 \times w
\][/tex]
[tex]\[
11200 = 5w
\][/tex]
6. Isolate [tex]\( w \)[/tex] by dividing both sides of the equation by 5:
[tex]\[
w = \frac{11200}{5}
\][/tex]
[tex]\[
w = 2240
\][/tex]
Therefore, the number of women at the college is 2240.
