Question

If PQ =20, QR = x+15 and PR = 4x-1 what is PR
Simpllify your answer and write it as a proper fraction mixed number or integer

Answer 1

To solve for \( PR \), we can start by using the fact that \( PQ + QR = PR \).

We are given the lengths:
- \( PQ = 20 \)
- \( QR = x + 15 \)
- \( PR = 4x - 1 \)

According to the segment addition postulate, we can write:

\[
PQ + QR = PR
\]

Substituting in the lengths we have:

\[
20 + (x + 15) = 4x - 1
\]

Now, simplify the left side:

\[
20 + x + 15 = 4x - 1
\]

This becomes:

\[
35 + x = 4x - 1
\]

Next, let's isolate \( x \) by moving \( x \) to the right side and \( -1 \) to the left side:

\[
35 + 1 = 4x - x
\]

This simplifies to:

\[
36 = 3x
\]

Now, divide both sides by 3:

\[
x = 12
\]

Now that we have \( x \), we can find \( PR \) using the expression for \( PR \):

\[
PR = 4x - 1
\]

Substituting \( x = 12 \):

\[
PR = 4(12) - 1
\]

Calculating:

\[
PR = 48 - 1 = 47
\]

So, \( PR = 47 \).

Thus, the value of \( PR \) is:

\[
\boxed{47}
\]