On a number line if r is less than s and if p is halfway between r and s and if t is halfway between p and r then what is the quotient of s minus t divided by t minus r?

Answer 1

The first half of the question yield two equations:

1.

I. p = r + (s - r) / 2

II. t = r + (p - r) / 2

The equation we are solving for, (s - t) / (t - r), does not have a p so we are going to Equation I for the pin Equation II. But first, to make things easier for us, let distribute the 2 in Equation II.

2. 2t = 2r + p - r

3. 2t = r + p

Substitute I

4. 2t = r + r + (s - r) / 2

5. 2t = 2r + (s - r) / 2

Again, lets distribute the 2, and combine the r's

6. 4t = 4r + s - r

7. 4t = 3r + s

In order to yield the desired quotient, we want a (s - t)on one side of the equation and (t - r) on the other. First let's get the (t - r) on the left.

8. 4t - 3r = s

9. t + 3t - 3r = s

10. t + 3(t - r) = s

Now move that extra t over to the right for the (s - t) we are looking for

11. 3(t - r) = s - t

Now divide both sides by (t - r) and we have our answer!

12. 3 = (s - t) / (t - r)