2006 CEMC Fermat Problems/Problem 2

Problem

If $2x + 3x + 4x = 12 + 9 + 6$ , then $x$ equals

$\text{ (A) }\ 6 \qquad\text{ (B) }\ 3 \qquad\text{ (C) }\ 1 \qquad\text{ (D) }\ \frac{1}{3} \qquad\text{ (E) }\ 10 \frac{1}{2}$

Combining the terms on the left and right sides, we get:

$9x = 27$

Dividing both sides by $9$ , we find that $x = \frac{27}{9} = \boxed {\textbf {(B) } 3}$ .

~anabel.disher

We can order the coefficients from greatest to least, like the terms on the right side of the equation:

$4x + 3x + 2x = 12 + 9 + 6$

We can notice that the numbers on the right are $3$ times the coefficients on the left. This can only occur if $x = \boxed {\textbf {(B) } 3}$ .

~anabel.disher