Question

In a day , a cafe sold cheese and vegetables sandwiches in the ratio $4:5$. It has sold $40$ cheese sandwiches. How many vegetable sandwiches were sold?

Answer 1

Given: Ratio of sold cheese and vegetable sandwich $=4:5$

Cheese sandwich sold $=40$

Let: vegetable sandwich sold be $=x$

It is written as $Cheese:vegetablesandwich=4:5$

$40:x:\hspace{0.17em}:4\hspace{0.17em}:5$

First and last term is called extreme terms, that is $40$ and $5$ and $x$ and $4$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 40\times 5=x\times 4 \\ x=\frac{40\times 5}{4} \\ x=\frac{{\displaystyle \stackrel{10}{\cancel{40}}\times 5}}{{\displaystyle \underset{1}{\cancel{4}}}} \\ x=10\times 5 \\ \therefore x=50 \end{gathered}$$

Hence the vegetable sandwiches are $50.$