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 per pound. he uses the equation 2x + 6y = 12 to represent the total cost, where x represents the number of pounds of granola and y represents the number of pounds of walnuts. he solves the 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 substituted the 3 for x when he should have substituted 6 for x. tomas added 6 to both sides of the equation instead of subtracting 6. tomas should have written the equation as 3x + 6y = 12. tomas substituted 3 for x when he should have substituted 3 for y.

Explanation:

Step1: Analyze the equation setup

The cost per pound of granola is $2, so the term for granola cost is \(2x\) (where \(x\) is pounds of granola). He bought 3 pounds of granola, so \(x = 3\). Substituting \(x = 3\) into \(2x\) gives \(2(3)=6\), which is correct so far.

Step2: Analyze the solving step

After substituting, the equation is \(6 + 6y=12\). To isolate the term with \(y\), we need to subtract 6 from both sides (since we have \(+6\) on the left). But Tomas added 6 to both sides (\(6 + 6y+6 = 12 + 6\)), which is the first error. Let's check other options:

• First option: \(x\) is pounds of granola, he bought 3 pounds, so substituting 3 for \(x\) is correct, not 6. Eliminate.
• Third option: The equation \(2x + 6y = 12\) is correct because granola is $2 per pound, so \(2x\) (not \(3x\)). Eliminate.
• Fourth option: \(x\) is granola pounds (3), \(y\) is walnuts pounds, so substituting 3 for \(x\) is correct, not for \(y\). Eliminate.

Answer:

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