Sunnyside Middle School wanted to add a new school sport, so they surveyed the students to determine which sport is most popular. Students were able to choose among soccer, football, lacrosse, or swimming. The same number of students chose lacrosse and swimming. The number of students who chose soccer was double the number of students who chose lacrosse. The number of students who chose football was triple the number of students who chose swimming. If 434 students completed the survey, how many students chose each sport?

Lacrosse = 62 students

Swimming = 62 students

Soccer = 124 students

Football = 186 students

Step-by-step explanation:

Based on the information, we can draw some equations

1.    Lacrosse = Swimming

2.   Soccer = 2 * Lacrosse

3.   Football = 3 * Swimming

4.   Football + Soccer + Swimming + Lacrosse = 434

Lets solve for once sport at a time, I will start with Football.

I will put equation 1, 2 and 3 into equation 4

3Sw + 2L + L + L = 434

We can now again put equation 1 into the new equation 4

3L + 2L + L + L = 434

Simplify

7L = 434

L = 434 ÷ 7

L = 62 students

Since L = Sw, 62 students did swimming also

We can put L into equation 2 to solve for So

So = 2 * 62

So = 124 students

And now we can put Sw into equation 3 to solve for F

F = 3 * 62

F = 186 students

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!