Chapter 5.7, Problem 40E

To determine

Tofind: The Total days for which dry dog food of one bag is sufficient to dog.

Answer to Problem 40E

Dry dog food of one bag is sufficient to dog for $38\frac{6}{13}\text{days}$ .

Explanation of Solution

Given information: Bag contains $40\text{cups}\text{of}\text{dry}\text{dog}\text{food}$ . Dog eat $\frac{3}{4}\text{cups}\text{of}\text{dry}\text{dog}\text{food}$ in the morning and $\frac{1}{3}\text{cups}\text{of}\text{dry}\text{dog}\text{food}$ in the night.

Calculation:

To calculate the total days till the food is last, it is needed to find the food eaten by dog in one day

Let the bag is sufficient for $x\text{days}$

  $\text{Food eaten by dog in one day=food eaten in the morning + food eaten in the night}$

  $\begin{array}{l}\Rightarrow \text{Food eaten by dog in one day}=\frac{1}{3}\text{cups}\text{of}\text{dry}\text{dog}\text{food+}\frac{3}{4}\text{cups}\text{of}\text{dry}\text{dog}\text{food}\\ \Rightarrow \text{Food eaten by dog in one day}=\frac{13}{12}\text{cups}\text{of}\text{dry}\text{dog}\text{food}\end{array}$

Therefore,

  $\begin{array}{l}\text{Food eaten by dog in one day}\times \text{ no}\text{. of days=bag contain total food}\\ \Rightarrow \frac{13}{12}\text{cup }\times x\text{ = 40 cup}\\ \Rightarrow x=40\times \frac{12}{13}\text{days}\\ \Rightarrow x=\frac{480}{13}\text{days}\\ \Rightarrow x=38\frac{6}{13}\text{days}\\ \end{array}$

Hence,

Dry dog food of one bag is sufficient to dog for $38\frac{6}{13}\text{days}$ .