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South African Mathematics Olympiad

Algebra Difficulty 3.8 AMC 10/12 Find the answer South Africa

On a line segment with the points $R$ , $A$ , $T$ and $E$ , the ratio $RA : AT = 1 : 3$ and $AT : TE = 5 : 2$ . The ratio $RA : TE$ is

Pick one

Solution

We are given $\frac{RA}{AT} = \frac{1}{3}$ and $\frac{AT}{TE} = \frac{5}{2}$ , so
$\frac{RA}{TE} = \frac{RA}{AT} \times \frac{AT}{TE} = \frac{1}{3} \times \frac{5}{2} = \frac{5}{6}.$

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