Question

The total number of parking spaces in a parking garage is calculated by adding the area of the lower level given by 22x2, the area of the upper level given by 20x2, and a compact car section given by 12x for a total of 414 parking spaces. Which equation could be used to solve for the number of compact car parking spaces?

Answer 1

Given:

Total number of parking spaces = 414
Area of lower level = 22x^2
Area of upper level = 20x^2
Compact car section = 12x

The total number of spaces in a parking garage = Area of lower level + area of upper level + area of compact car section.

Working equation:

414 = 22x^2 + 20x^2 + 12x
414 = 42x^2 + 12x
42x^2 + 12x - 414 = 0

solve for x

x1 = 3
x2 = -3.29

We can only use the positive value. Therefore, x = 3. The number of compact car parking spaces is 12x = 12 * 3 = 36 parking spaces

The complete data set is:

Lower level parking = 22x^2 = 198
Upper level parking = 20x^2 = 180
Compact parking space = 12x = 36