Competition problem — Algebra — Maths Olympiad Prep

Algebra Difficulty 3.8 AMC 10/12 Find the answer Italy

Problem:

Two numbers $a$ and $b$ are such that $\frac{3a+b}{a-b}=2$ . What is the value of $\frac{a^{3}}{b^{3}}$ ?

Pick one

Solution

Solution:

The answer is $(\mathbf{A})$ . We have $3a+b=2a-2b$ , so $a=-3b$ , and therefore $\frac{a^{3}}{b^{3}}=(-3)^{3}=-27$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement translated into English from the original; metadata (topic, difficulty) added by this project.