Question

How do you write a problem that can be solved using proportions? Write the proportion and solve the problem.

Answer 1

Hint: Here we will take an example that will include the concept of proportion. Such type of question will include two ratios equated with each other and the formula used will be: - product of mean is equal to product of extreme.

Complete step by step answer:
Here we have been to write a problem that involves the concept of proportion and we need to solve the problem also.
Let us take an example. So we say, if 12 buckets of paint is used to paint a wall having area $30m^2$ then we have to determine the buckets of paint that will be required to paint a wall having area $75m^2$.
Now let us solve this simple example. Let us assume that we need x number of buckets to paint $75m^2$ of wall. We can think of the approach used in the unitary method to solve this question. We can say that if 12 bucket is used for painting $30m^2$ wall then the fraction of wall that can be painted with 1 bucket will be ${\displaystyle \frac{30}{12}}{m}^2$. Similarly, if x buckets of paint will be used to paint $75m^2$ of wall then the fraction of wall than will be painted using 1 bucket will be ${\displaystyle \frac{75}{x}}{m}^2$. Now, this fraction of area will remain same for both the cases because in the end we are using only 1 bucket of paint, so we will have the relation in proportion form as $30:12::75:x$ which is equivalent to the equation ${\displaystyle \frac{30}{12}}={\displaystyle \frac{75}{x}}$. We need to solve for the value of x.
Cross multiplying the terms we get
$\Rightarrow 30x=12\times 75$
Dividing both the sides with 30 we get,
$\begin{array}{rl}& \Rightarrow x={\displaystyle \frac{12\times 75}{30}}\\ & \therefore x=30\end{array}$

Hence, 30 buckets of paint will be used.

Note: Remember that ratio and proportion uses the concept of the unitary method. In the above example the relation $30:12::75:x$ has its own certain terms. Here, 12 and 75 are called mean and 20 and x are called extreme. So, there is an important formula that arises which is that the product of mean is equal to the product of extremes. You can think of a different approach also, like in the above solution we have found the area painted due to 1 bucket, you may also find the number of buckets used to paint $1m^2$ wall. In this case the terms will get inverted on both the sides of the proportion and we will get the relation $12:30::x:75$. The only thing to note is that the unit of area must get cancelled on both the sides.