Question

Marina can make 36 cupcakes in 45 minutes. How long will it take for her to make 108 cupcakes?

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 time taken to make 108 cupcakes, we need to consider the time taken to make 36 cupcakes i.e., considering with respect to ratio and proportions and then finding the unknown variable i.e., time taken to make 108 cupcakes.

Complete step by step answer:
Given, Marina can make
36 cupcakes in 45 minutes i.e.,
\[ \to \] 36 cupcakes = 45 minutes …………………. 1
And we need to find the time taken to make 108 cupcakes, hence let \[x\] be the time taken to make 108 cupcakes i.e.,
\[ \to \] 108 cupcakes = \[x\] minutes ………………. 2
To find the time taken to make 108 cupcakes, we need to consider the time taken to make 36 cupcakes. Now, let us write equation 1 and 2 in terms of ratio as both are equivalent i.e.,
\[ \Rightarrow 36:45 = 108:x\]
Hence, to solve the proportion is rewritten as:
\[\dfrac{{36}}{{45}} = \dfrac{{108}}{x}\]
Now, we need to cross multiply and solve for x as:
\[36\left( x \right) = 108\left( {45} \right)\]
Multiplying the terms, we get
\[36x = 4860\]
Now, divide both sides of the expression by 36 as:
\[\dfrac{{36x}}{{36}} = \dfrac{{4860}}{{36}}\]
Hence, simplifying the common terms we get:
\[x = \dfrac{{4860}}{{36}}\]
\[ \Rightarrow x = 135\] minutes or 2 hours 15 minutes

Therefore, it takes 135 minutes for her to make 108 cupcakes.

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.