Using proportions, it is found that Trisha owns 28 pairs of socks.
To solve this problem, we will use the proportion, them combine it with a system of equations.
System variables:
- Variable x: Number of pairs of fluffy socks she owns.
- Variable y: Number of pairs of regular socks she owns.
What is the proportion?
- Trisha owns 2 pairs of fluffy socks for every 5 pairs of regular socks, hence, the proportion is:
[tex]\frac{x}{y} = \frac{2}{5}[/tex]
[tex]2y = 5x[/tex]
[tex]y = \frac{5x}{2}[/tex]
Trisha owns 12 more pairs of regular socks than fluffy socks, hence:
[tex]y = 12 + x[/tex]
[tex]\frac{5x}{2} = 12 + x[/tex]
[tex]5x = 24 + 2x[/tex]
[tex]3x = 24[/tex]
[tex]x = \frac{24}{3}[/tex]
[tex]x = 8[/tex]
Then:
[tex]y = \frac{5x}{2} = \frac{5(8)}{2} = 20[/tex]
The total amount is: 8 + 20 = 28.
Hence, Trisha owns 28 pairs of socks.
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
