Question

Kyle asks his friend Jane to guess his age and his grandmother’s age. Kyle says his grandmother is not more than 80 years old. He says his grandmother’s age is, at most, 3 years less than 3 times his own age.

Jane writes this system of inequalities to represent k, Kyle’s age, and g, Kyle’s grandmother’s age.

Inequality 1: g > 80
Inequality 2: g ≤ 3k – 3
Which inequality did Jane write incorrectly, and how could it be corrected?

Inequality 1 is incorrect; it should be g ≤ 80.
Inequality 1 is incorrect; it should be g ≥ 80.
Inequality 2 is incorrect; it should be g < 3k – 3.
Inequality 2 is incorrect; it should be g ≥ 3k – 3.

Answer 1

Answer: Inequality 1 is incorrect; it should be g ≥ 80.

The correct inequalities should be:

Inequality 1: g ≥ 80 (since Kyle's grandmother is not more than 80 years old)

Inequality 2: g ≤ 3k - 3 (since Kyle's grandmother's age is at most 3 years less than 3 times his own age)