If AB and CD are the same distance, BC is twice the distance of either of these two and DE is triple this length, what percentage of the line is BD?

Question

Quizplus · Accepted Answer

In order to solve this problem, we have to create an equation that represents the relationship between the different parts of the line. First, we read that AB and CD are the same distance. We can label both AB and CD as x since it is an unknown value. So, AB = x CD = x Next, we read that BC is twice the distance of either AB or CD. Since AB and CD both have a value of x, we can write the value of BC as 2x. So, AB = x CD = x BC = 2x Lastly, we read that DE is triple the distance or length of either AB or CD. Since AB and CD both have a value of x, we can write the value of DE as 3x. So, AB = x CD = x BC = 2x DE = 3x Now, we need to determine the total length of the line. x + x + 2x + 3x = 7x There are seven parts to the line. Before we can calculate the percentage, we have to determine the length of BD. BD is a combination of BC and CD, and we do know the lengths of those. We can simply add those two values together. AB = x CD = x BC = 2x DE = 3x So, BD = 2x + x = 3x Finally, we can determine what percentage of the line is the segment BD. We start out with our percentage formula (remember that the fraction line represents division): % = ^part/_whole• 100 Our whole is the total length of the line. The part is the length of the segment BD. % = ³/₇• 100 Divide ³/₇ and round to the nearest tenth to make the percent a whole number. % = .43• 100 % = 43 Answer: Segment BD is 43% of the line.

If AB and CD Are the Same Distance, BC Is