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 leq 3k - 3 ). which inequality did jane write incorrectly, and how could it be corrected? - inequality 1 is incorrect, it should be ( g leq 80 ). - inequality 1 is incorrect, it should be ( g geq 80 ). - inequality 2 is incorrect, it should be ( g < 3k - 3 ). - inequality 2 is incorrect, it should be ( g geq 3k - 3 ).

Explanation:

1. Analyze Kyle's first statement: "his grandmother is not more than 80 years old" means her age \(g\) is less than or equal to 80, so \(g \leq 80\). Jane wrote \(g > 80\) for Inequality 1, which is wrong.
2. Analyze Kyle's second statement: "his grandmother's age is, at most, 3 years less than 3 times his own age" translates to \(g \leq 3k - 3\), which matches Jane's Inequality 2, so this one is correct.

Answer:

Inequality 1 is incorrect, it should be \(g \leq 80\)