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Sagot :
#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.
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.
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