canbtg wrote:During a certain month, Dave watched n two-hour movies and r ninety-minute movies. Had he spent the same amount of time watching television, he could have watched 60 thirty-minute television shows. Each of the following is a possible ratio of n to r EXCEPT
A)3:16
B)1:2
C)2:3
D)9:8
E)3:1
Total time for 60 30-minute shows = 60*30 = 1800 minutes.
Since n 120-minute shows and r 90-minute shows must sum to 1800 minutes, we get:
120n + 90r = 1800
12n + 9r = 180
4n + 3r = 60.
A) n:r = 3:16
Substituting n=3 and r=16 into 4n + 3r = 60, we get:
4*3 + 3*16 = 60.
60 = 60.
This works.
Eliminate A.
B) n:r = 1:2
Substituting n=1 and r=2 into 4n + 3r = 60, we get:
4*1 + 3*2 = 60
10 = 60.
For the lefthand side to equal the righthand side, the lefthand side must increase by a factor of 6.
The implication is that n and r much each increase by a factor of 6, to n=6 and r=12.
Substituting n=6 and r=12 into 4n + 3r = 60, we get:
4*6 + 3*12 = 60
60 = 60.
This works.
Eliminate B.
C: n:r = 2:3
Substituting n=2 and r=3 into 4n + 3r = 60, we get:
4*2 + 3*3 = 60
17 = 60.
For the lefthand side to equal the righthand side, the lefthand side must increase by a factor of 60/17.
The implication is that n and r much each increase by a factor of 60/17, to n=120/17 and r=180/17.
Not possible, since n and r must be INTEGER values.
The correct answer is
C.
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