Question

example 3

1. family maria is 11 inches shorter than her sister clara. luna is 11 inches shorter than her brother chad. if maria is shorter than luna, how do the heights of clara and chad compare? what else can be concluded if maria and luna are the same height?

Explanation:

Step1: Define Variables

Let \( M \) be Maria's height, \( C_a \) be Clara's height, \( L \) be Luna's height, and \( C_h \) be Chad's height.
From the problem, we have:
\( M = C_a - 11 \) (Maria is 11 inches shorter than Clara)
\( L = C_h - 11 \) (Luna is 11 inches shorter than Chad)

Step2: Compare Clara and Chad when \( M < L \)

Substitute the expressions for \( M \) and \( L \) into \( M < L \):
\( C_a - 11 < C_h - 11 \)
Add 11 to both sides of the inequality:
\( C_a - 11 + 11 < C_h - 11 + 11 \)
Simplify:
\( C_a < C_h \)
So Clara is shorter than Chad.

Step3: Compare Clara and Chad when \( M = L \)

Substitute the expressions for \( M \) and \( L \) into \( M = L \):
\( C_a - 11 = C_h - 11 \)
Add 11 to both sides of the equation:
\( C_a - 11 + 11 = C_h - 11 + 11 \)
Simplify:
\( C_a = C_h \)
So Clara and Chad have the same height.

Answer:

When Maria is shorter than Luna, Clara is shorter than Chad (\( C_a < C_h \)). When Maria and Luna are the same height, Clara and Chad have the same height (\( C_a = C_h \)).