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

From the question given,

Area of the parking lot = 300 square meters

Bicycle requirement = 3 square meters

Bus requirement = 9 square meters

Total number of vehicle = 40 vehicles

Let x be the number of bicycles and y be the number of bus

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

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

We can solve by elimination method

Multiply through equation (1) by 3 in other to eliminate x and then we will solve for y

3x + 3y = 180----------------------------(3)

Equation (2) - Equation (3)

6y = 180

Divide both-side by 6

y = 30

substitute y=30 into equation (1) and solve for x

x + 30 = 40

subtract 30 from both-side

x = 40 -30

x=10

Number of bicycle is 10 and number of bus is 30

Since, a bicycle is charged $1.50 and bus is $3

Then the total income is;

$(10 × 1.50 + 30 × 3)

= $(15 + 90)

= $105

Therefore, the the possible income region is $105.