Question

Preeta watches an ant and beetle crawl in a hole in the ground. the beetle is 3/4 inch below ground level. the beetle climbs 1/3 the distance the ant is below the ground level. the beetle is now 2 1/2 inches below ground level. Let X be the position of the ant relative to ground level. what equation can be written to solve for X? solve the equation.​

Answer 1

Answer:

1a:  $\frac{3}{4}$ + $\frac{1}{3}x$ = $2\frac{1}{2}$

1b: See below

1c:  $2\frac{3}{4}$ 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:

$\frac{3}{4}$ + $\frac{1}{3}x$ = $2\frac{1}{2}$

1b. Solve the equation written above from 1a.

$\frac{3}{4}$ + $\frac{1}{3}x$ = $2\frac{1}{2}$

-3/4     -3/4   [subtract 3/4 to start the process of getting x by itself]

$\frac{1}{3}x$ = 1$\frac{3}{4}$

*3/1   *3/1 [Multiply Reciprocal to get X by itself]

x= $5\frac{1}{4}$

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 =  $2\frac{3}{4}$