Question

28 of the 38 participants in a triathlon are men and the rest are women. what is the ratio of the number of men participating to the number of women participating? write your answer as two numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Find number of women

Total participants: 38, Men: 28. So women = 38 - 28 = 10.

Step2: Find ratio of men to women

Men : Women = 28 : 10. Simplify by dividing both by 2: 14 : 5. Wait, no, 28 and 10 have GCD 2? Wait 28 ÷ 2 =14, 10 ÷2=5? Wait no, 38-28=10? Wait 28+10=38? 28+10=38, yes. Wait but 28 and 10: GCD is 2? Wait 28 ÷ 2=14, 10 ÷2=5. Wait but wait, 28 and 10: let's check again. Wait 38 participants, 28 men, so women are 38 -28 =10. So ratio of men to women is 28:10. Simplify by dividing numerator and denominator by 2: 14:5? Wait no, 28 and 10: GCD is 2? Wait 28 ÷ 2 =14, 10 ÷2=5. But wait, 28 and 10: 28/10 = 14/5? Wait no, 28 divided by 2 is 14, 10 divided by 2 is 5. So 14:5? Wait but wait, maybe I made a mistake. Wait 38-28=10? 28+10=38, yes. So men are 28, women 10. So ratio 28:10. Simplify by dividing both by 2: 14:5. Wait but let's check GCD of 28 and 10. Factors of 28: 2,2,7. Factors of 10:2,5. So GCD is 2. So divide both by 2: 14:5. Wait but wait, maybe the problem is 28 men, 38 total, so women 10. So ratio men:women is 28:10, which simplifies to 14:5? Wait no, 28 and 10: 28 ÷ 2 =14, 10 ÷2=5. So 14:5. Wait but let's check again. Wait 28 men, 10 women. So 28:10. Divide numerator and denominator by 2: 14:5. Yes.

Answer:

14:5