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.