Question

A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than the number of rows in the lot. The mayor has requested that the new lot should hold twice as many cars as the current parking lot, which has space for 56 cars.

Determine which equation the civil engineer can use to find the number of rows, x, he should include in the new parking lot.

A.
x2 - 6x = 112
B.
6x2 - 56 = 112
C.
x2 - 6 = 112
D.
2x2 - 12x = 112

Answer 1

A.
`\displaystyle x^2 - 6x = 112`

Step-by-step explanation:

"each row should be six less than the number of rows" →
`\displaystyle x - 6`

"twice as many cars as the current parking lot, which has space for 56 cars" → 112 >> [2][56]

`\displaystyle x[x - 6] = 112 → x^2 - 6x = 112`

I am joyous to assist you anytime.

Answer 2

Explanation:

The new parking lot must hold twice as many cars as the previous parking lot. The previous parking lot could hold 56 cars. So this means the new parking lot must hold 2 x 56 = 112 cars

Let y represent the number of cars in each row, and x be the number of total rows in the parking lot. Since the number of cars in each row must be 6 less than the number of rows, we can write the equation as:

y = x - 6 (1)

The product of cars in each row and the number of rows will give the total number of cars. So we can write the equation as:

xy = 112 (2)

Using the above two equations, the civil engineer can find the number of rows he should include in the new parking lot.

Using the value of y from equation 1 to 2, we get:

x(x - 6) = 112 (3)

This equation is only in terms of x, i.e. the number of rows and can be directly solved to find the number of rows that must in new parking lot.