Question

CD = 69, BC = 10x + 3. AD = 18x + 44,and AB= 7x- 20. Find BC.

Answer 1

Answer: A) 83

Explanation:

Representing this segments in a number line, and supposing that they are arranged in alphabetical order:

Here we can see that if we sum all of the segments they must be equal to 18x+44:

$7x-20+10x+3+69=18x+44$

Combining like terms:

$17x+52=18x+44$

Now we move all of the terms with x to the right side and all of the independent numbers to the left side:

$\begin{gathered} 52-44=18x-17x \\ 8=x \end{gathered}$

And now that we know the value of x, we can find BC:

$\begin{gathered} BC=10x+3 \\ BC=10(8)+3 \\ BC=80+3 \\ BC=83 \end{gathered}$

Which is option A)