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Re: M07-04 [#permalink]
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Bunuel wrote:
At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams. If Roofy gets 9 points after missing a pipe and Ralph gets 7 points after missing a pipe and a beam, how many points does Butch get if he misses 4 jumps but goes through the rest of the exercises perfectly?

A. 8.2
B. 8.4
C. 8.8
D. 9.0
E. 9.2


4P+10J+2B=10

When we miss one Pipe, the points scored is 9.

Therefore, P=1.

Now when the dog misses 1 Pipe and 1 Beam, the points scored is 7. We already know P is 1 that means B=2.

So 10J=2.
J=2/10
J=0.2

So when the dog misses 4 Jumps he loses 0.8 points and scores 9.2 which is option E.
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M07-04 [#permalink]
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I don't see a step-by-step answer in the comments, so I'll post one for those who need it.

From the prompt:

#1) 4P+10J+2B=10
#2) 3P+10J+2B=9
#3) 3P+6J+2B=7

We're asked how many points 4P+6J+2B yeilds.

Subtract equation #3 from equation #2:

3P+10J+2B=9
-3P+10J+1B=7
B=2

Substitute B=2 in equations #1 and #2, then subtract #2 from #1:

#1)
4P+10J+2(2)=10
4P+10J+4=10
4P+10J=6

#2)
3P+10J+2(2)=9
3P+10J+4=9
3P+10J=5

Subtract equation #2 from equation #1:

4P+10J=6
-3P+10J=5
P=1

Substitute P=1 & B=2 into equation #1:

4(1)+10J+2(2)=10
4+10J+4=10
10J+8=10
10J=2
J=(2/10)=(1/5)

Now we know that P=1, J=(1/5) and B=2; we can substitute the values in equation 4P+6J+2B to solve the problem

4(1)+6(1/5)+2(2)
4+(6/5)+4
8+(6/5)
(40/5)+(6/5)
46/5 = 9 & 1/5 = 9.2

The correct answer is answer choice E.­
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Re: M07-04 [#permalink]
I think this is a high-quality question.
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Re: M07-04 [#permalink]
I think this is a high-quality question and I agree with the explanation
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Re: M07-04 [#permalink]
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re M07-04 [#permalink]
I think this is a high-quality question and I agree with explanation.
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Re: M07-04 [#permalink]
 
Desertchampion wrote:
I don't see a step-by-step answer in the comments, so I'll post one for those who need it.


From the prompt:

#1) 4P+10J+2B=10
#2) 3P+10J+2B=9
#3) 3P+6J+2B=7

We're asked how many points 4P+6J+2B yeilds.

Subtract equation #3 from equation #2:

3P+10J+2B=9
-3P+10J+1B=7
B=2

Substitute B=2 in equations #1 and #2, then subtract #2 from #1:

#1)
4P+10J+2(2)=10
4P+10J+4=10
4P+10J=6

#2)
3P+10J+2(2)=9
3P+10J+4=9
3P+10J=5

Subtract equation #2 from equation #1:

4P+10J=6
-3P+10J=5
P=1

Substitute P=1 & B=2 into equation #1:

4(1)+10J+2(2)=10
4+10J+4=10
10J+8=10
10J=2
J=(2/10)=(1/5)

Now we know that P=1, J=(1/5) and B=2; we can substitute the values in equation 4P+6J+2B to solve the problem

4(1)+6(1/5)+2(2)
4+(6/5)+4
8+(6/5)
(40/5)+(6/5)
46/5 = 9 & 1/5 = 9.2


The correct answer is answer choice E.




Please give kudos if this was helpful in any way!

­
Because only 1 variable changes between equations (#1 and #2, #2 and 3#) you know that the variation in the amount of points corresponds to the variation of the variable.
With that, you can quickly know that P=1 and B=2. Then you find J with any of the equations and calculate the points of the dog.
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