Question

1. zoe and claire are sisters. they are giving clues about their heights. write an equation and solve to determine the height of both zoe and claire.

#1: claire is twice as tall as zoe.
#2: together, claire and zoe are 108 inches tall.

Explanation:

Step1: Define variables

Let \( z \) be Zoe's height (in inches) and \( c \) be Claire's height (in inches). From clue #1, \( c = 2z \).

Step2: Set up the equation

From clue #2, the sum of their heights is 108, so \( c + z = 108 \). Substitute \( c = 2z \) into this equation: \( 2z + z = 108 \).

Step3: Solve for \( z \)

Combine like terms: \( 3z = 108 \). Divide both sides by 3: \( z=\frac{108}{3}=36 \).

Step4: Find Claire's height

Substitute \( z = 36 \) into \( c = 2z \): \( c = 2\times36 = 72 \).

Answer:

Zoe's height is 36 inches, Claire's height is 72 inches.