Question

2. the student to faculty ratio at a small college is 17:3 the total of students and faculty is 740 how many faculty members are there at college? how many students?
3. the speedy fast ski resort has started to keep track of the number of skiers and snowboarders who bought season passes. the ratio of the number of skiers who bought season passes to the number of snowboarders who bought season passes is 1:2. if 1259 more snowboarders bought season passer than skiers, how many snowboarders ams how many skiers bought season passes?

Answer 1

#2) 629 students and 111 faculty. #3) 1259 skiers and 2518 snowboarders.

Explanation:
#1) Let S be the number of students and F be the number of faculty. S/F = 17/3.
We know that S+F = 740; subtracting F from both sides, we have S=740-F. We can use this to rewrite the proportion:
(740-F)/F=17/3.

Cross multiply:
3(740-F)=17(F).

Using the distributive property, we have
3*740-3*F=17F; 2220-3F=17F.

Add 3F to both sides:
2220-3F+3F=17F+3F
2220=20F.

Divide both sides by 20:
2220/20 = 20F/20
111=F.

There are 111 faculty members. Substitute that into our equation, S=740-F: S=740-111
S=629.

#2) Let x be the number of skiers. We know that there were 1259 more snowboarders with passes than skiers; that gives us x+1259.
The ratio of skiers to snowboarders is 1/2; this gives us the proportion x/(x+1259)=1/2.

Cross multiply:
2(x)=1(x+1259)
2x=x+1259.

Subtract x from both sides
2x-x=x+1259-x
x=1259.

There were 1259 skiers. This means there were 1259+1259=2518 snowboarders.