Question

To make a scenery, Ashok mixes \[6\] bottles of white paint with $8$ bottles of green paints, for every $3$ bottles of white paint, how many bottles of green paint does he mix?

Answer 1

Hint: Identify the known and unknown ratios and set up the proportion and solve accordingly. Convert the word statements in the form of mathematical expressions and simplify for the required solution.

Complete step-by-step answer:
Given that- Ashok mixes \[6\] bottles of white paint with $8$ bottles of green paints to make the scenery.
Therefore, we can say that for every \[6\] bottles of white paint, Ashok used $8$ bottles of green paints.
We can expressed it in the ration form as –
$\dfrac{{6{\text{ white paint}}}}{{8{\text{ Green paint}}}} = \dfrac{6}{8}$
Take common factors both from the numerator and the denominator and remove it.
$ \Rightarrow \dfrac{{6{\text{ white paint}}}}{{8{\text{ Green paint}}}} = \dfrac{3}{4}$
Hence, for every $3$ bottles of white paint, Ashok mixes $4$ bottles of green paint.

Additional Information:
 Ratio is the comparison between two numbers without any units. Whereas, when two ratios are set equal to each other are called proportion. Four numbers a, b, c, and d are said to be in proportion. If $a:b = c:d$ whereas, four numbers are said to be in continued proportion if $a:b = b:c = c:d$.


Note: Always convert the given word statement in the correct mathematical form and simplify using basic mathematical operations. In case of any unknown ratios, suppose any variable for the reference value. Since, here when the ration was converted in the reduced form taking common factors, we got the required answer. It is always not the same case, at times it may be the equivalent form of the given fraction where you have to find by using multiples.