Question

A café has three different sizes of plate. The ratio of small to medium is 2:5 and the ratio of medium to large is 3:4What is the ratio of small plates, to medium plates to large plates?

Answer 1

6: 15 : 20

Explanation:

Ratio of small to medium = 2 : 5

Ratio of medium to large = 3 : 4

We need to make the medium in both ratios equivalent since medium is common to both:

$\begin{gathered} \frac{small}{\text{medium}}\text{ = }\frac{2}{5} \\ \frac{medium}{\text{large}}=\frac{3}{4} \\ \text{for medium to be equivalent, we multiply ratio by 3} \\ we\text{ multiply the second ratio by 5} \\ \text{LCM = 3}\times5\text{ = 15} \end{gathered}$

We multiply the numerator by same amount we multiply the denuominator in both ratios:

$\begin{gathered} \frac{small}{\text{medium}}\text{ = }\frac{2}{5}\times\frac{3}{3}\text{ } \\ \frac{small}{\text{medium}}=\text{ }\frac{6}{15} \\ \\ \frac{medium}{\text{large}}=\frac{3}{4}\times\frac{5}{5} \\ \frac{medium}{\text{large}}=\text{ }\frac{15}{20} \end{gathered}$

The ratio of small to medium to large:

$\begin{gathered} \text{The medium is the same so we can bring all thr}ee\text{ together:} \\ \text{small: medium: large} \\ 6\colon\text{ 15 : 20} \end{gathered}$