Question

A bike is on sale for $\$170$. This is 80% of the regular price. How do you find the regular price?

Answer 1

Hint: A ratio is a mathematical expression written in the form of \[a:b\], where a and b are any integers and b is not equal to 0 and it expresses a fraction. To find the regular price of the bike, we need to consider the given data that, the price of bike is $170, and bike is 80% of the regular price, hence considering this we need to find the unknown variable x i.e., regular price of the bike.

Complete step by step solution:
Given,
A bike is on sale for 170 i.e.,
\[ \Rightarrow \] Price of bike = 170.
Price of bike is 80% of the regular price i.e.,
\[ \Rightarrow \] 80% of x.
Let the regular price of bike be x. and hence, we need to find the regular price;
From, the given data we have:
\[x \cdot 80\% = 170\]
As, the given value is in percentage, hence to convert the percentage value i.e., 80% as\[\dfrac{{80}}{{100}}\], hence we have:
\[ \Rightarrow x \cdot \dfrac{{80}}{{100}} = 170\]
\[ \Rightarrow x = \dfrac{{170 \times 10}}{8}\]
Multiplying the terms, we get:
\[ \Rightarrow x = \dfrac{{1700}}{8}\]
\[ \Rightarrow x = 212.50\]

Therefore, the regular price of bike is $212.50.

Note: The ratio should exist between the quantities of the same kind. While comparing two things, the units should be similar. There should be significant order of terms and the comparison of two ratios can be performed, if the ratios are equivalent like the fractions. Hence, in this way we need to solve the question, comparing with the given data.