Question

The recipe of making 3 dozen muffins requires 1.5 cups of flour. How many cups of flour are required to make 5 dozen muffins?

Answer 1

Hint: We are given that the recipe of 3 dozen muffins is prepared by using 1.5 cups of flour. We have to find the number of cups required to make 5 dozen muffins. To answer this, we will first learn about the unitary method. We work on them with some examples. After getting a grip on it, we will work on our problem. We will first find the flour required for 1 dozen muffins.

Complete step by step solution:
We are given that a recipe for making muffins needs 1.5 cups of flour for 3 dozen muffins. We have to find the quantity of flour to make 5 dozen muffins. To answer this, we learn about the unitary method. Unitary method is a technique which helps to form a link between the cost of 1 quantity with the cost of any number of quantities. In this method, we can find the cost for 1 unit of quantity from the given $n$ number of quantities. Similarly, we can find the cost of $n$ quantity if we are aware about the cost of 1 unit.
Now, to solve our problem, we will use the same technique. We are given that 3 dozen muffins need 1.5 cups of flour. So, we are given the flour for 3 dozen. We will use the unitary method to convert it to get the flour needed for 1 dozen. So, we have,
3 dozen = 1.5 cups of flour
Dividing both sides by 3, we get,
$\dfrac{3}{3}$ dozens = $\dfrac{1.5}{3}$ cups of flour
So, we get,
1 dozen muffins = 0.5 cups of flour.
So, we get that 1 dozen muffins will be requiring 0.5 cups of flour. Now we will again use a unitary method to find the flour needed for 5 dozen. Now, as we have,
1 dozen = 0.5 cups of flour,
So, to get the amount of flour for 5 dozen muffins, we multiply it by 5, so we have,
5 dozen = 0.5 $\times $ 5 = 2.5
5 dozens = 2.5 cups of flour.
So, we get 5 dozen muffins which will require 2.5 cups of flour.

Note: We have to remember that we cannot directly multiply the term by 5 to get the flour required for 5 dozen muffins. That is, if we do 5 $\times $ 1.5 = 7.5 cups, then we will be getting an incorrect solution. Also, when we change we need to be careful with the unit and dimension. The term should be in the same unit during the entire solution.