To determine which equations model the total yards of fabric Sophie will buy, let’s analyze each combination of red fabric ([tex]\(x\)[/tex]) and blue fabric ([tex]\(y\)[/tex]) provided in the table.
1. For the combination (1, 27):
[tex]\[
x + y = 1 + 27 = 28
\][/tex]
This equation holds true. So, [tex]\(x + y = 28\)[/tex] is a valid equation.
2. For the combination (2, 26):
- Checking [tex]\(28 + x = y\)[/tex]:
[tex]\[
28 + 2 = 30 \neq 26
\][/tex]
This equation is not valid.
- Checking [tex]\(x - y = 28\)[/tex]:
[tex]\[
2 - 26 = -24 \neq 28
\][/tex]
This equation is not valid.
3. For the combination (3, 25):
- Checking [tex]\(28 - x = y\)[/tex]:
[tex]\[
28 - 3 = 25
\][/tex]
This equation holds true.
4. For the combination (4, 24):
[tex]\[
x + y = 4 + 24 = 28
\][/tex]
This equation holds true. So, [tex]\(x + y = 28\)[/tex] is a valid equation again.
Based on the analysis, the valid equations that model the total yards of fabric Sophie will buy are:
- [tex]\(x + y = 28\)[/tex]
- [tex]\(28 - x = y\)[/tex]
