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M07-04
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16 Sep 2014, 00:34
16 Sep 2014, 00:34
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Difficulty:
35%
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Question Stats:
77% (02:24) correct
23%
(02:40)
wrong
based on 631
sessions
At a dog competition, a dog is awarded 10 points for successfully completing three exercises: running through 4 pipes, making 10 jumps, and walking on 2 beams. If Roofy earns 9 points after missing one pipe but completing the rest of the exercises perfectly, and Ralph earns 7 points after missing one pipe and one beam but completing the rest of the exercises perfectly, how many points does Butch earn if he misses 4 jumps but completes the rest of the exercises perfectly?
A. 8.2
B. 8.4
C. 8.8
D. 9.0
E. 9.2
A. 8.2
B. 8.4
C. 8.8
D. 9.0
E. 9.2
Re M07-04
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16 Sep 2014, 00:34
16 Sep 2014, 00:34
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Official Solution:
At a dog competition, a dog is awarded 10 points for successfully completing three exercises: running through 4 pipes, making 10 jumps, and walking on 2 beams. If Roofy earns 9 points after missing one pipe but completing the rest of the exercises perfectly, and Ralph earns 7 points after missing one pipe and one beam but completing the rest of the exercises perfectly, how many points does Butch earn if he misses 4 jumps but completes the rest of the exercises perfectly?
A. 8.2
B. 8.4
C. 8.8
D. 9.0
E. 9.2
A dog is awarded 10 points for successfully completing three exercises: running through 4 pipes (p), making 10 jumps (j), and walking on 2 beams (b). The total points equation can be expressed as \(4p + 10j + 2b = 10\).
Roofy earns 9 points after missing one pipe, which means missing one pipe reduces the points by 1. So, \(p = 1\).
Ralph earns 7 points after missing one pipe and one beam, which means missing one pipe and one beam reduces the points by 3. Therefore, \(p + b = 3\). Since \(p = 1\), we have \(b = 2\).
Substituting these values into \(4p + 10j + 2b = 10\) gives \(4*1 + 10j + 2*2 = 10\), which simplifies to \(j = 0.2\). Therefore, if Butch misses 4 jumps but completes the rest of the exercises perfectly, he will earn \(10 - 4j =10 - 4*0.2 = 9.2\) points.
Answer: E
At a dog competition, a dog is awarded 10 points for successfully completing three exercises: running through 4 pipes, making 10 jumps, and walking on 2 beams. If Roofy earns 9 points after missing one pipe but completing the rest of the exercises perfectly, and Ralph earns 7 points after missing one pipe and one beam but completing the rest of the exercises perfectly, how many points does Butch earn if he misses 4 jumps but completes the rest of the exercises perfectly?
A. 8.2
B. 8.4
C. 8.8
D. 9.0
E. 9.2
A dog is awarded 10 points for successfully completing three exercises: running through 4 pipes (p), making 10 jumps (j), and walking on 2 beams (b). The total points equation can be expressed as \(4p + 10j + 2b = 10\).
Roofy earns 9 points after missing one pipe, which means missing one pipe reduces the points by 1. So, \(p = 1\).
Ralph earns 7 points after missing one pipe and one beam, which means missing one pipe and one beam reduces the points by 3. Therefore, \(p + b = 3\). Since \(p = 1\), we have \(b = 2\).
Substituting these values into \(4p + 10j + 2b = 10\) gives \(4*1 + 10j + 2*2 = 10\), which simplifies to \(j = 0.2\). Therefore, if Butch misses 4 jumps but completes the rest of the exercises perfectly, he will earn \(10 - 4j =10 - 4*0.2 = 9.2\) points.
Answer: E
General Discussion
Re: M07-04
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28 Nov 2016, 11:31
28 Nov 2016, 11:31
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Here is how I did it:
Clearly, from the info,
One pipe missed lead to 9 points. So, 4 pipes are worth 4 points in total.
2 beams are worth 4 points as well in total, since missing one beam lead to a loss of 2 points.
That's 8 points so far. 2 points remaining.
Consequently, 10 jumps = 2 points.
10j = 2
j = 2/10 = 1/5. This is the value of each jump.
Butch only misses 4 jumps, but does the rest of the exercise perfectly.
So, his 8 points are secure. From the 4 jumps he's missed, his loss in points will be: 4 * 1/5 = 4/5 = 0.80.
10-0.80 = 9.20.
Clearly, from the info,
One pipe missed lead to 9 points. So, 4 pipes are worth 4 points in total.
2 beams are worth 4 points as well in total, since missing one beam lead to a loss of 2 points.
That's 8 points so far. 2 points remaining.
Consequently, 10 jumps = 2 points.
10j = 2
j = 2/10 = 1/5. This is the value of each jump.
Butch only misses 4 jumps, but does the rest of the exercise perfectly.
So, his 8 points are secure. From the 4 jumps he's missed, his loss in points will be: 4 * 1/5 = 4/5 = 0.80.
10-0.80 = 9.20.
