If AB and CD are the same distance, BC is twice the distance of either of these two, DE is triple this length and the total length of the line segment is 56 cm, what is the length of the segment CE?

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. Total line segment length = 7x.
We are told that the length of the line segment is 56 in. In order to determine the length of an individual segment of this line, we need to find the value of x.
We know that the line segment is equal to both 56 in and 7x, as we found above.  Therefore, we can set these two values equal to one another and solve for x.
56 = 7x
Divide both sides by 7 in order to isolate the variable (x).
56 ÷ 7 = 7x ÷ 7
8 = x
Now that we know the value of x, we can plug it in to solve the problem.
We are asked to find the length of CE. This is not one of the values given to us, but we can figure it out by using our visual. Looking at the line segment, we can see that CE is the combination of CD and DE.
Based on our work above, we know what CD = x and DE = 3x. We can find CE by adding these two together.
x + 3x = CE
Now, plug in our x value.
8 + 3(8) = CE
8 + 24 = CE
32 = CE

If AB and CD Are the Same Distance, BC Is