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Tomas is making trail mix using granola and walnuts. He can spend a total of [tex]$12 on the ingredients. He buys 3 pounds of granola that costs $[/tex]2.00 per pound. The walnuts cost $6 per pound. He uses the equation [tex]\(2x + 6y = 12\)[/tex] to represent the total cost, where [tex]\(x\)[/tex] represents the number of pounds of granola and [tex]\(y\)[/tex] represents the number of pounds of walnuts. He solves the equation for [tex]\(y\)[/tex], the number of pounds of walnuts he can buy.

[tex]\[
\begin{aligned}
2x + 6y &= 12 \\
2(3) + 6y &= 12 \\
6 + 6y + 6 &= 12 + 6 \\
6y &= 18 \\
y &= 3
\end{aligned}
\][/tex]

Which is the first error that Tomas made?

A. Tomas substituted the 3 for [tex]\(x\)[/tex] when he should have substituted 6 for [tex]\(x\)[/tex].

B. Tomas added 6 to both sides of the equation instead of subtracting 6.

C. Tomas should have written the equation as [tex]\(3x + 6y = 12\)[/tex].

D. Tomas substituted 3 for [tex]\(x\)[/tex] when he should have substituted 3 for [tex]\(y\)[/tex].

Sagot :

GinnyAnswer
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.
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