Question

of the 50 parking spots in the garage, 28 are empty. what is the ratio of the number of empty parking spots to the number of full parking spots? write your answer as two numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Find the number of full parking spots

Total parking spots are 50, and empty ones are 28. So full spots = \( 50 - 28 = 22 \).

Step2: Find the ratio of empty to full spots

The ratio of empty to full spots is \( 28:22 \). Simplify by dividing both by 2: \( \frac{28}{2}:\frac{22}{2} = 14:11 \). Wait, no, the problem says "ratio of the number of empty parking spots to the number of full parking spots". So empty is 28, full is 22. So ratio is 28:22, simplify: divide numerator and denominator by 2, get 14:11? Wait, no, 28 and 22 have a GCD of 2. 28 ÷ 2 =14, 22 ÷2=11. Wait, but let's check again. Total spots 50, empty 28, so full is 50 -28 =22. So ratio of empty to full is 28:22. Simplify: divide both by 2, 14:11. Wait, but maybe I misread. Wait the problem says "ratio of the number of empty parking spots to the number of full parking spots". So empty is 28, full is 22. So 28:22, simplify to 14:11. Wait, but let's check the calculation again. 50 -28 is 22. So 28 and 22. GCD of 28 and 22 is 2. So 28 ÷2=14, 22 ÷2=11. So the ratio is 14:11? Wait, no, wait 28:22 can be simplified by dividing both by 2, so 14:11. Wait, but maybe I made a mistake. Wait 28 and 22: 28 is 2×14, 22 is 2×11. So yes, 14:11. Wait, but let's check the problem again. "Of the 50 parking spots in the garage, 28 are empty. What is the ratio of the number of empty parking spots to the number of full parking spots?" So empty is 28, full is 50 -28=22. So ratio empty:full =28:22=14:11. Wait, but maybe the problem wants it as 28:22, but simplified. So 14:11. Wait, but let's do it step by step.

Wait, first, find full spots: 50 -28 =22. Then ratio of empty to full is 28:22. Simplify by dividing numerator and denominator by 2: 14:11. So the ratio is 14:11? Wait, no, 28 and 22, GCD is 2. So 28 ÷2=14, 22 ÷2=11. So yes, 14:11.

Wait, but maybe I messed up the subtraction. 50 -28: 50 -20=30, 30 -8=22. Correct. So full is 22. So ratio empty:full is 28:22=14:11.

Answer:

14:11