Question

Martha has 20 t-shirts that are white, blue or red. The number of red shirts is one more than twice the number of blue shirts. The number of white shirts is 2 less than the number of red shirts. Write a system of linear equations that can be used to determine the possible numbers of each color of shirts.

Answer 1

To solve this problem, we can set up a system of linear equations.

1. First, we define the variables:
Let W represent the number of white shirts.
Let B represent the number of blue shirts.
Let R represent the number of red shirts.

2. According to the problem, Martha has a total of 20 shirts in all colors. So, our first equation is derived from the total number of shirts:
W (white shirts) + B (blue shirts) + R (red shirts) = 20

3. Secondly, we know from the problem that the number of red shirts is one more than twice the number of blue shirts. We can express this information as an equation:
R (red shirts) = 2B (twice the number of blue shirts) + 1

4. Lastly, the problem tells us that the number of white shirts is two less than the number of red shirts. We can write this as another equation:
W (white shirts) = R (red shirts) - 2

So, the system of equations that represent the given conditions is:
1) W + B + R = 20
2) R = 2B + 1
3) W = R - 2

Now these equations can be solved to find W, B and R which represent the number of white, blue and red shirts respectively.