Chapter 6.1, Problem 41IP

a.

To determine

Calculate the number of cell phones with keyboards that will added to the stores inventory.

Answer to Problem 41IP

The number of phones added to the inventory is $5$ .

Explanation of Solution

Given:

It is given in the question that there will be $120$ cell phones in stock out of these $45$ have keyboards, the manager wants to increase the inventory such that $40\%$ of the stock has keyboards.

Concept Used:

In this, use the concept of percent proportion such that the ratio of given two number will equal to the ratio of $p/100$ .

Calculation:

Here,

It has to add a number x of cell phones so that $40\%$ of cell phones have keyboards. So add x to both the cell phones with keyboards and to the total number of cell phones.

So,

  $\begin{array}{l}\frac{45+x}{120+x}=\frac{40}{100}\\ (45+x)\cdot 100=(120+x)\cdot 40\\ 4500+100x=4800+40x\\ 100x-40x=4800-4500\\ 60x=300\\ x=\frac{300}{60}\\ x=5\end{array}$

Conclusion:

The number of phones added is $5$ .

b.

To determine

Find the total number of cell phones in stock.

Answer to Problem 41IP

The number of cell phone in the inventory is $75$ .

Explanation of Solution

Given:

It is given in the question that the value of $x=5$ .

Concept Used:

In this, put the given value in the variable equation and get the result.

Calculation:

Here,

Total inventory = $120+5=125$

Total number of keyboard = $45+5=50$

Net number of cell phones = $125-50=75$

Conclusion:

The number of cell phone is $75$ .