all of my shoes are red except 2 all of my shoes are blues except 2 all of my shoes are brown except 2 how many pairs of shoes do i have?
To solve this problem, we need to analyze the information given.
Let's denote the number of red shoes as R, the number of blue shoes as B, and the number of brown shoes as Br. According to the given information, we can form equations based on the following statements:
- All of my shoes are red except 2: R - 2 = B + Br (Equation 1)
- All of my shoes are blue except 2: B - 2 = R + Br (Equation 2)
- All of my shoes are brown except 2: Br - 2 = R + B (Equation 3)
We can now solve this system of equations to find the values of R, B, and Br.
First, let's substitute Equation 1 into Equation 2 and simplify:
(B + Br) - 2 = R + Br
B - 2 = R (Equation 4)
Substituting Equation 4 into Equation 3:
Br - 2 = B + (B - 2)
Br - 2 = 2B - 2
Br = 2B
Now, substitute this expression for Br into Equation 1:
R - 2 = B + 2B
R - 2 = 3B
R = 3B + 2 (Equation 5)
We now have a relationship between R and B.
From here, we can make some observations to find the values that satisfy the equations. We know that the number of shoes cannot be negative, and the problem statement implies that we have at least two pairs of each color. So, let's start with a minimum of 2 pairs for each color and see if that gives a valid solution.
Assuming we have 2 pairs for each color:
- R = 2 * 3 + 2 = 8
- B = 2
- Br = 2 * 2 = 4
Therefore, we would have a total of 8 red shoes, 2 blue shoes, and 4 brown shoes. Each pair consists of two shoes. Thus, the total number of pairs would be:
(8 + 2 + 4) / 2 = 14 / 2 = 7 pairs.
So in this scenario, you would have 7 pairs of shoes.