At a certain university, the football program receives 4 times more fu

Football program receives 4 times more funding than does the basketball program:
F=B+4*B=5B
Together, the football and basketball programs receive 3 times as much funding as do all other sports programs :
F+B=3*(Other)
3*(Other)=5B+B=6B
Others= 2 *B
the ratio of funding for the basketball program to funding for all other sports programs, not including the football program :
B/(other)= B/(2B) = 1/2 ?

The first statement in the question says football receives 4 times more funding than basketball and not 4 times as much. This implies the difference between football funding and basketball funding is 4 times the basketball funding.

F - B = 4*B (assuming F and B are the fundings received by football and basketball respectively)
F = 5*B ------(1)

Further, the question says funding for football and basketball is 3 times as much as all the other sport's funding.
F + B = 3*A (assuming A is the fund received by all other sports)
=> 6*B = 3*A (from (1))
=> A = 2B ----- (2)

The question asks to find the ratio of funds received by basketball to all other sports i.e. B:A
=> B:2B (from (2))
= 1:2

I am not sure why 1:2 is not even in the answer choice.

Solution

Given

• The football program receives 4 times more funding than does the basketball program.
• The football and basketball programs receive 3 times as much funding as do all other sports programs combined.

To Find

• The ratio of funding for the basketball program to funding for all other sports programs, not including the football program

Approach and Working Out

• The let funding in basketball be B.

o That in football is 4B.
o Football + basketball = 5B
• Let other sports be X,

o Football + Basketball = 3X
• Now both 3X and 5B are equal hence we can take a common multiple of 3 and 5 for easier approach.

o That is 15.
o 5B = 15
o Basketball, B = 3
o Football, B = 12
• Again, 3X = 15

o So, X = 5
• Basketball : Other sports (without football) = 3 : 5

Correct Answer: Option C

At a certain university, the football program receives 4 times more funding than does the basketball program. Together, the football and basketball programs receive 3 times as much funding as do all other sports programs combined. What is the ratio of funding for the basketball program to funding for all other sports programs, not including the football program?

A. 1:5
B. 1:4
C. 3:5
D. 3:4
E. 5:3

Stem : the football program receives 4 times more funding than does the basketball program: Football/Basketball = 4X/X(X is the common multiplier)
the football and basketball programs receive 3 times as much funding as do all other sports programs combined. = 3Y/Y (Y is the common multiplier)
Combining ratios : Football + Basketball = 4X + X = 5X (Multiple of 5)
Also Football + Basketball = 3Y (Multiple of 3)
So, \(F/B\) @X = 15 \(4X/X\) = \(60/15\)
F + \(B/Others\) = \(3Y/Y\) = 60 + \(15/Y\) = 3 * \(25/25\) (As y is a multiple of 3)
Therefore B/Others - Football = 15/25 =3 : 5
C