Video Transcript
Find the value of 𝑎 given the following
information: 𝑌 is on the line between 𝑋 and 𝑍. 𝑋𝑌 equals 24 centimeters, 𝑌𝑍 equals
eight 𝑎 centimeters, and 𝑋𝑍 equals 88 centimeters.
We can begin this question by drawing the
line 𝑋𝑍 on which 𝑌 lies. We’re told that 𝑋𝑌 equals 24
centimeters, 𝑌𝑍 equals eight 𝑎 centimeters, and the length of the whole line 𝑋𝑍 is 88
centimeters. The length from 𝑋𝑌 plus the length from
𝑌𝑍 is equal to the total distance from 𝑋 to 𝑍. As all of our measurements are in
centimeters, this can be written as an equation. 24 plus eight 𝑎 is equal to 88. We can then solve this equation to
calculate the value of 𝑎. We begin by subtracting 24 from both
sides. As 88 minus 24 is equal to 64, we have
eight 𝑎 equals 64. We can then divide both sides of this new
equation by eight. This gives us the value of 𝑎 equal to
eight.
We can check this by substituting this
value back in. From the line above, we actually know
that eight 𝑎 is equal to 64. This means that the length of the line
from 𝑌 to 𝑍 is 64 centimeters. As 24 centimeters plus 64 centimeters
equals 88 centimeters, our answer is correct.
