could someone help me with some math?

Question

I just need someone to explain these three problems.

1. Participation in team sport in a certain college was up 25% at the end of last year, but participation in individual sports like tennis were down 25 %. The ratio of students participating in team sports to students taking part in individual sports was how many times grater at the end of the year than the ratio at the beginning of the year?

2. What is the ratio of the circumference of circle to its radius?
A. 1
B. (pi)/2
C. sqrt (pi)
D. pi
E. 2*(pi)

3. 40 gallons of a certain mixture is made up of 3 parts of water and 5 parts of Liquid X. if the mixture must be changed in order to be 75% Liquid X, how many gallons of Liquid X must be added to the origianl mixture?
A) 15
B) 20
C) 35
D) 50
E) 60

Answer 1

1)
at the beginning of the year, the ratio was
t / i. (team / individual)

At the end of the year,
team sports was up 25% = (5/4)t
indiv sports were down 25% = (3/4)i

(5/4)t / (3/4)i
= 5t / 3i
= (5/3)(t/i)

So the ratio at the end of the year was 5/3 times greater than the beginning of the year.

2)
C = 2(radius)(pi)

2(radius)(pi) : radius
2(pi) : 1

Answer is E.

3)
Right now, you have 5/8 liquid X. 5/8 of 40 = 25 gallons, so the ratio fo liquid X to total gallons is
25 / 40

You are going to add y gallons of liquid X to this to get 75% mixture (75% = 3/4)...

(25 + y) / (40 + y) = 3/4
(25 + y)(4) = 3(40 + y)
100 + 4y = 120 + 3y
100 + y = 120
y = 20 gallons

Answer 2

1. 1.666_ times. The initial ratio is 100% times as big as the original ratio, so the new ratio is 125%/75%=1.666_ (one and two thirds) times as big as the initial ratio (because 100%+25%=125% and 100%-25%=75%).
2. E. Pi is defined as being the ratio between the circumference and diameter of a circle, and the radius is half the diameter, so the answer is 2pi.
3. B. There are 8 parts total, and 40/8=5 gallons per part, 3*5=15 of those gallons are water, so for 15 to be 100%-75%=25% of the total there have to be 15/25%=15*4=60 gallons total, so the amount to be added is 60-40=20 gallons.

Easy enough to understand?

Answer 3

1.) 1.25/.75 = 1 2/3
2.) C/r = 2pi
3.) 20 gallons this would make 45/60 = 3/4 = 75%

Answer 4

2. circumfrence is 2pir, so the answer is E

3.