Question

The area of a parking lot is 300 square meters. A bicycle requires 3 square meters. A bus requires 9 square meters. The parking lot can hold only 40 vehicles. If a bicycle is charged $1.50 and a bus $3, find the possible income region.

Answer 1

Given:

• Area of the parking lot = 300 m²
• Bicycle requires an area of 3 m²
• Bus requires an area of 9 m²
• Total number of vehicles = 40

To find: The possible income.

Solution:

Let the number of bicycles is x and that of buses is y.

Then,

x + y = 40 .....(1)

3x + 9y = 300 .....(2)

From (2), we get

x + 3y = 100 .....(3)

Now, (3) - (1) gives

x + 3y - x - y = 100 - 40

or, 2y = 60

or, y = 30

Putting y = 30 in (1), we get

x + 30 = 40

or, x = 10

So, number of bicycles = 10,

number of buses = 30.

Given, a bicycle is charged $1.50 and a bus $3.

Thus total income is

= $(10 × 1.50 + 30 × 3)

= $(15 + 90)

= $105

Answer: If a bicycle is charged $1.50 and a bus $3, the possible income region is $105.