CEMC Fermat, 2023

Algebra Difficulty 1.4 Junior Find the answer Canada

If $a(x+2)+b(x+2)=60$ and
$a+b=12$ , then $x$ is equal to

Pick one

Solution

The equation $a(x+2) + b(x+2) = 60$ has a common factor of $x+2$ on the left side.

Thus, we can re-write the equation as $(a+b)(x+2) = 60$ .

When $a+b = 12$ , we obtain $12 \cdot (x+2) = 60$ and so $x + 2 = 5$ which gives $x = 3$ .

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