Let's go through Tomas' calculations step-by-step to determine where he made the first mistake.
1. The initial equation representing the total cost is:
[tex]\[
2x + 6y = 12
\][/tex]
2. Tomas buys 3 pounds of granola, which implies:
[tex]\[
x = 3
\][/tex]
3. Substituting [tex]\(x = 3\)[/tex] into the equation:
[tex]\[
2(3) + 6y = 12
\][/tex]
4. This simplifies to:
[tex]\[
6 + 6y = 12
\][/tex]
5. At this point, Tomas should solve for [tex]\(y\)[/tex] by isolating [tex]\(6y\)[/tex]. He should subtract 6 from both sides of the equation. However, Tomas mistakenly added 6 to both sides. His steps were:
[tex]\[
6 + 6y + 6 = 12 + 6
\][/tex]
6. This leads to:
[tex]\[
6y = 18
\][/tex]
7. Solving [tex]\(6y = 18\)[/tex] gives:
[tex]\[
y = 3
\][/tex]
The correct steps Tomas should have taken after reaching [tex]\(6 + 6y = 12\)[/tex] are:
1. Subtract 6 from both sides:
[tex]\[
6 + 6y - 6 = 12 - 6
\][/tex]
2. This simplifies to:
[tex]\[
6y = 6
\][/tex]
3. Solving [tex]\(6y = 6\)[/tex] gives:
[tex]\[
y = 1
\][/tex]
Hence, the first error Tomas made was adding 6 to both sides of the equation instead of subtracting 6.
So, the correct answer is:
- Tomas added 6 to both sides of the equation instead of subtracting 6.
