Question

The ratio of skiers to snowboarders is 1:2. There are 1250 more snowboarders than skiers. How many skiers and snowboarders are there?

Answer 1

There are 1250 skiers and 2500 snowboarders. The student's question was a math problem requiring setting up a system of equations based on a given ratio and difference in quantities.

Step-by-step explanation:

The student is asking a problem that involves setting up and solving a system of equations. With the given ratio of skiers to snowboarders being 1:2, we can represent the number of skiers as 's' and the number of snowboarders as '2s'. Based on the information that there are 1250 more snowboarders than skiers, we can formulate the equation '2s = s + 1250'. Solving for 's', we first subtract 's' from both sides to get 's = 1250'. This means there are 1250 skiers. To find the number of snowboarders, we substitute the value of 's' into the equation '2s', which gives us '2 * 1250 = 2500'. Therefore, there are 2500 snowboarders.

Answer 2

`x-number\ of\ skiers\\x+1250-numbers\ of\ snowboarders\\\\(skiers)/(snowboarders)=(1)/(2)\Rightarrow(x)/(x+1250)=(1)/(2)\ \ \ \ |cross\ multiply\\\\2x=x+1250\ \ \ \ \ \ |subtract\ x\ from\ both\ sides\\\\x=1250\\\\x+1250=1250+1250=2500\\\\Answer:There\ are\ 1250\ skiers\ and\ 2500\ snowboarders.`