Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

If $a=\frac{2}{3}b$ and $b \neq 0$ , what is $\frac{9a+8b}{6a}$ equal to?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $a=\frac{2}{3}b$ , then $3a=2b$ . Since $b \neq 0$ , then $a \neq 0$ . Thus, $\frac{9a+8b}{6a}=\frac{9a+4(2b)}{6a}=\frac{9a+4(3a)}{6a}=\frac{21a}{6a}=\frac{7}{2}$ . Alternatively, $\frac{9a+8b}{6a}=\frac{3(3a)+8b}{2(3a)}=\frac{3(2b)+8b}{2(2b)}=\frac{14b}{4b}=\frac{7}{2}$ .

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