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. 2 x plus 6 y is equal to 12 2 times 3 plus 6 y is equal to 12 6 plus 6 y plus 6 is equal to 12 plus 6 6 y is equal to 18 y is equal to 3 Which is the first error that Tomas made?
Answer
A
Tomas should have written the equation as 3 x plus 6 y is equal to 12 .
B
Tomas added 6 to both sides of the equation instead of subtracting 6 .
C
Tomas substituted 3 for x when he should have substituted 3 for y .
D
Tomas substituted the 3 for x when he should have substituted 6 for x .
Explanation
The equation 2x + 6y = 12 is correct because granola costs $2 per pound and walnuts cost $6 per pound. Substituting x = 3 gives 6 + 6y = 12. To isolate 6y, Tomas should subtract 6 from both sides, not add 6; this is his first error. The correct choice is B, “Tomas added 6 to both sides of the equation instead of subtracting 6.”
AI-written and checked against the verified answer.