Answer:
1a: [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
1b: See below
1c: [tex]2\frac{3}{4}[/tex] inches between the beetle and ant
Step-by-step explanation:
1a. To build the equation, we need to see that the beetle started at 3/4th inches below ground level, then "climbed" (which is poor English, it should be descended) a certain distance, and then it ended up at 2 1/2 inches below ground. The distance "climbed" can be represented as 1/3X, where "X" is the ant's current distance. We would do 1/3rd times "X" to figure out how much the beetle climbed down.
So that means, if we added together the starting position of 3/4, plus the distance the beetle descended (1/3X), that would get us TO 2 1/2 inches below ground (the beetle's new current position). So therefore our equation is:
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
1b. Solve the equation written above from 1a.
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
-3/4 -3/4 [subtract 3/4 to start the process of getting x by itself]
[tex]\frac{1}{3}x[/tex] = 1[tex]\frac{3}{4}[/tex]
*3/1 *3/1 [Multiply Reciprocal to get X by itself]
x= [tex]5\frac{1}{4}[/tex]
1c. So we take the position of the ant figured out on 1b (5 1/4 inches), and the new current position of the beetle (2 1/2 inches), and subtract them
5 1/4 - 2 1/2 = [tex]2\frac{3}{4}[/tex]
