a new parking lothas spaces for 450 cars. the ratio of spaces for fullsized cars to compact cars is 11 to 4. how many spaces are for full-sized cars? how many spaces for compact cars?

Say there are 11x big cars.

Then there are 4x small cars

11x+4x = 450

solve for x
Then you can get 4x easily.

To find the number of spaces for full-sized cars and compact cars, we need to understand and compute the ratio between them.

The given ratio is 11 to 4, which means for every 11 spaces for full-sized cars, there are 4 spaces for compact cars.

Let's assign variables to the number of spaces for full-sized and compact cars.

Let f represent the number of spaces for full-sized cars.
Let c represent the number of spaces for compact cars.

Based on the given ratio, we can write the equation:

f/c = 11/4

To find the values of f and c, we need to solve this equation. The total number of spaces in the parking lot is 450, so we know that:

f + c = 450

To solve this system of equations, we can use substitution:

From the first equation, we can isolate f:

f/c = 11/4
=> f = (11/4) * c

Now substitute f in the second equation:

(11/4) * c + c = 450

To simplify the equation, multiply every term by 4 to eliminate the fractions:

11c + 4c = 450 * 4
15c = 1800

Divide both sides of the equation by 15:

c = 1800/15
c = 120

Now substitute the value of c back into the equation for f:

f = (11/4) * c
f = (11/4) * 120
f = 11 * 30
f = 330

Therefore, there are 330 spaces for full-sized cars and 120 spaces for compact cars in the parking lot.