Question

# You can rent books at a local store for $5.00 each. An Internet company offers a flat fee of $20.00 per month for as many books as you want. How many books do you need to rent to make the online rental a better buy?

Hint:

### Total cost of renting = number of books Rate per book.

## The correct answer is: We need to rent more than 4 books to make the online rental a better buy.

### Step-by-step solution:-

Let the number of books to be bought in a month be x.

∴ Total cost incurred for renting at local store = Number of books × cost per book

∴ Total cost incurred for renting at local store = x × $5 ..................................................... (From given information)

∴ Total cost incurred for renting at local store = 5x ........................................................... (Equation i)

Also,

Total cost incurred on internet company for a month = $20 .................. (From given information) ..................... (Equation ii)

We need to find the number of books to be rented to make the online rental a better buy.

i.e. we need to find the value of x for which-

Cost incurred at local store > Cost incurred on online rental

∴ 5x > 20 ...................................................................................... (From Equations i & ii)

∴ x > 20/5 .................................................................................. (Dividing both sides by 5)

∴ x > 4

We need to rent more than 4 books to make the online rental a better buy.

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**Note:**

There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.

Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?

**Note:**

There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

### Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.

Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.

Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.

¶A line's slope can be determined using its two points (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

### Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.

Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.

Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.

¶A line's slope can be determined using its two points (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

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Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.

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**Note:**

A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.

Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.

If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?

**Note:**

A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.