Question

tomas is making trail mix using granola and walnuts. he can spend a total of $12 on the ingredients. he buys 3 pounds of granola that costs $2.00 per pound. the walnuts cost $6 pound. he uses the equation $2x + 6y = 12$ to represent the total cost, where $x$ represents number of pounds of granola and $y$ represents the number of pounds of walnuts. he solves equation for $y$, the number of pounds of walnuts he can buy.
$2x + 6y = 12$
$2(3) + 6y = 12$
$6 + 6y + 6 = 12 + 6$
$6y = 18$
$y = 3$
which is the first error that tomas made?

• tomas added 6 to both sides of the equation instead of subtracting 6.
• tomas substituted 3 for $x$ when he should have substituted 3 for $y$.
• tomas should have written the equation as $3x + 6y = 12$.
• tomas substituted the 3 for $x$ when he should have substituted 6 for $x$.

Explanation:

Step1: Analyze the equation solving steps

The original equation is \(2x + 6y=12\). After substituting \(x = 3\), we get \(2(3)+6y = 12\), which simplifies to \(6 + 6y=12\). To solve for \(y\), we need to isolate the term with \(y\). The correct operation here is to subtract 6 from both sides, because we have \(6+6y = 12\), and we want to get rid of the 6 on the left - hand side. So we should do \(6 + 6y-6=12 - 6\), not \(6 + 6y + 6=12 + 6\) as Tomas did.

Step2: Evaluate other options

• Option 2: \(x\) represents the number of pounds of granola and he bought 3 pounds of granola, so substituting 3 for \(x\) is correct, not for \(y\).
• Option 3: The cost of granola is \(\$2\) per pound, so the term for granola cost is \(2x\) (where \(x\) is pounds of granola), so the equation \(2x + 6y = 12\) is correct.
• Option 4: The cost per pound of granola is \(\$2\), not \(\$6\), so substituting 6 for \(x\) is wrong.

Answer:

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