Official Solution:

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


Create three equations:
\(4P + 10J + 2B = 10\)
\(3P + 10J + 2B = 9\)
\(3P + 10J + 1B = 7\)

By subtracting #2 from #1 and #3 from #1 we find out that \(P = 1\) and \(P + B = 3\), \(B = 2\). Therefore, \(J = 0.2\) and Butch will get \(10 - (0.2*4) = 9.2\) points.


Answer: E
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Hi Bunuel

Is there any handy concept I can apply to such kind of probs involving 2 or 3 linear equations? Because I am struggling often to figure out what to substract from what or whether I need to multiply at all.

Thank you

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.

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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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!

I think this is a high-quality question.

Let X- no of pipes, Y - no of jumps, Z - no of beams

4x+10y+2z=10

given 3x+10y+2z=9 -> From above 2 statments, X = 1
given 3x+10y+z=7 -> From above 2 statments, Z=2 -> Y=0.2

4X+6Y+2Z= 4*1 + (6/5) + 2*2 = 9.2

I think this is a poor-quality question and I agree with explanation. Where is it written that the scores are lineal? For example, the first mistake might be less penalised than the second
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If he missed 4 jumps then wouldn't he be left with 6 jumps. Leading you to the answer of C?

I think this is a high-quality question and I agree with the explanation