Ratio riddle
Can you work out the ratio b:c given the ratios a:b and a:c?
Age
14 to 16
Challenge level
Problem
The ratio $a : b = 2 :3$ and the ratio $a : c = 3 : 4$. What is the ratio $b : c$? If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $9 : 8$
Image
$a : b$
$2 : 3$ (given)
$a\hspace{2.9mm}:\hspace{2.9mm}c$
$3\hspace{2.9mm}:\hspace{2.9mm}4$ (given)
$a:b:c$
$6:9:8$ (since $3\times2=2\times3=6$)
Using fractions
$$\frac{b}{c} = \frac{a}{c} \times\frac{b}{a}= \frac{3}{4} \times\frac{3}{2} = \frac{9}{8}$$