Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

If $a(x+2)+b(x+2)=60$ and $a+b=12$ , what is the value of $x$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

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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