Question

cumulative review
define a - b - c (b is between a and c) as follows. 1.4 - 1.5

1. using set notation
2. using an algebraic statement
3. given c - p - d, if cd = 152 in. and cp is 4 in. more than three times pd, find cp and pd.

Explanation:

Step1: Set up variables

Let \( PD = x \) inches. Then \( CP=3x + 4 \) inches.

Step2: Use the segment - addition postulate

Since \( C - P - D \), by the segment - addition postulate \( CD=CP + PD \). Substitute \( CD = 152\), \(CP=3x + 4\) and \(PD=x\) into the equation:

$$152=(3x + 4)+x$$

Step3: Simplify the equation

Combine like terms: \(152 = 4x+4\).
Subtract 4 from both sides: \(152-4=4x\), so \(148 = 4x\).

Step4: Solve for \(x\)

Divide both sides by 4: \(x=\frac{148}{4}=37\).

Step5: Find \(CP\)

Substitute \(x = 37\) into \(CP=3x + 4\). Then \(CP=3\times37+4=111 + 4=115\).

Answer:

\(CP = 115\) inches and \(PD = 37\) inches.