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Point A,B,C, and D lie on a single line in that order. The length of BC is p percent of AB. The length of BC is 25% of the length of CD. The length of AD is 20. What is p?

A) 10
B) 20
C) 30
D) 40
E) cannot be determined

User Sebres
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1 Answer

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To solve for p, we can set up an equation using the given information. By rearranging the equation and solving for p, we find that p cannot be determined without knowing specific values for CD and x. Therefore, the answer is E) cannot be determined.

To solve for p, we need to use the given information to set up an equation.

Let's say the length of AB is x. According to the problem, BC is p% of AB, so the length of BC is px/100.

It is also given that BC is 25% of CD, so BC is (25/100)*CD.

Since points A, B, C, and D lie on a single line, we can write the equation: AB + BC + CD = AD.

Substituting the lengths, we have x + px/100 + (25/100)*CD = 20.

Now we can solve for p.

Expanding the equation gives us x + px/100 + 0.25*CD = 20.

Factoring out x, we have x(1 + p/100) + 0.25*CD = 20.

Since the question asks for p, we can isolate p by first subtracting x from both sides: px/100 + 0.25*CD = 20 - x.

Then, we multiply both sides by 100 to eliminate the fraction: px + 25CD = 2000 - 100x.

Rearranging the equation, we get px + 100x = 2000 - 25CD.

Combining like terms gives us (p + 100)x = 2000 - 25CD.

Finally, we can solve for p by dividing both sides by x: p + 100 = (2000 - 25CD) / x.

This equation gives us the value of p in terms of CD and x.

Since we are not given the specific values of CD or x, we cannot determine the exact value of p. Therefore, the answer is E) cannot be determined.

User Martin Moser
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