Question

Every day, a sweet shop uses \[13\dfrac{1}{3}\] bags of sugar to make sweets. For how many days will 145 bags of sugar last?

Answer 1

Hint: Here, we will assume the number of days to be \[x\]. We will convert the number of bags used per day into an improper fraction. The total number of bags of sugar will be equal to the product of the number of bags used per day and the number of days. Using this and the given information, we will get an equation in terms of \[x\]. We will simplify this equation to get the value of \[x\] and hence, the number of days the 145 bags will last.

Complete step-by-step answer:
Let the number of days be \[x\].
Now, it is given that the number of bags used each day is \[13\dfrac{1}{3}\] bags.
First, we will convert this mixed fraction to improper fraction.
Therefore, we get
\[\begin{array}{l}13\dfrac{1}{3} = \dfrac{{3 \times 13 + 1}}{3}\\ \Rightarrow 13\dfrac{1}{3} = \dfrac{{40}}{3}\end{array}\]
Thus, we get the number of bags of sugar used each day as \[\dfrac{{40}}{3}\] bags.
Now, we know that the total number of bags of sugar will be equal to the product of the number of bags used per day and the number of days.
Therefore, we can form the equation
Total number of bags \[ = \] Bags used per day \[ \times \] Number of days
Substituting the total number of bags as 145, the number of days as \[x\], and the number of bags used each day as \[\dfrac{{40}}{3}\] in the above equation, we get
\[ \Rightarrow 145 = \dfrac{{40}}{3}x\]
Multiplying both sides of the equation by 3, we get
\[\begin{array}{l} \Rightarrow 145 \times 3 = \dfrac{{40}}{3}x \times 3\\ \Rightarrow 435 = 40x\end{array}\]
Dividing both sides of the equation by 40, we get
\[\begin{array}{l} \Rightarrow \dfrac{{435}}{{40}} = \dfrac{{40x}}{{40}}\\ \Rightarrow 10.875 = x\end{array}\]
\[\therefore \] The 145 bags will last \[10.875\] days.
This can be written as \[10.875 = 10\dfrac{7}{8}\] days in fraction form.

Note: Here, we converted a mixed fraction to an improper fraction. An improper fraction is a fraction whose numerator is larger than its denominator. A mixed fraction is a fraction in the form \[a\dfrac{b}{c}\]. Every mixed fraction \[a\dfrac{b}{c}\] can be converted to an improper fraction \[\dfrac{{c \times a + b}}{c}\]. We can also convert an improper fraction to decimal form by dividing the numerator by the denominator of the improper fraction.