Problem 5: A sports event features 250 athletes. 1/5 of the athletes are sprinters, 1/4 are long-distance runners, and the remainder are field event athletes.
What fraction of the athletes are sprinters and long-distance runners?
How many athletes are sprinters and long-distance runners?
How many athletes are field event athletes?
视频信息
答案文本
视频字幕
Let's solve this step by step. We have 250 athletes in a sports event. One-fifth are sprinters, one-fourth are long-distance runners, and the remainder are field event athletes. We need to find the fraction and number of sprinters plus long-distance runners, and the number of field event athletes.
First, we need to add the fractions for sprinters and long-distance runners. To add one-fifth and one-fourth, we need a common denominator. The least common multiple of 5 and 4 is 20. Converting the fractions: one-fifth equals four-twentieths, and one-fourth equals five-twentieths.
Now let's calculate the actual numbers. For sprinters and long-distance runners combined, we multiply nine-twentieths by 250, which gives us 112.5 athletes. For field event athletes, the remaining fraction is eleven-twentieths. Multiplying eleven-twentieths by 250 gives us 137.5 field event athletes.
Let's verify our solution. We calculated 50 sprinters, 62.5 long-distance runners, and 137.5 field event athletes. Adding these together: 50 plus 62.5 plus 137.5 equals 250, which matches our total. Our final answers are: the combined fraction of sprinters and long-distance runners is nine-twentieths, the combined number is 112.5 athletes, and there are 137.5 field event athletes.
To summarize our complete solution: First, the fraction of athletes who are sprinters and long-distance runners combined is nine-twentieths. Second, the number of athletes who are sprinters and long-distance runners is 112.5. Third, the number of field event athletes is 137.5. This problem demonstrates how to work with fractions in real-world contexts and verify our answers by checking that all parts add up to the total.