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

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

Which is the first error that Tomas made?

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

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

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

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



Answer :

GinnyAnswer
Let's carefully analyze the problem and the steps Tomas took to solve the equation.

First, recall the equation Tomas used:
[tex]\[ 2x + 6y = 12 \][/tex]
He then substituted [tex]\( x = 3 \)[/tex] (since he bought 3 pounds of granola at $2 per pound):
[tex]\[ 2(3) + 6y = 12 \][/tex]
[tex]\[ 6 + 6y = 12 \][/tex]

At this point, Tomas made his first mistake. Here is what he wrote and the error within it:
[tex]\[ 6 + 6y + 6 = 12 + 6 \][/tex]
By looking closely, we notice that Tomas incorrectly added 6 to both sides of the equation instead of subtracting 6 from both sides. The correct step should have been:
[tex]\[ 6 + 6y - 6 = 12 - 6 \][/tex]
[tex]\[ 6y = 6 \][/tex]
[tex]\[ y = 1 \][/tex]

So, the first error that Tomas made was adding 6 to both sides of the equation instead of subtracting 6. Thus, the correct answer is:
Tomas added 6 to both sides of the equation instead of subtracting 6.