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
Answer
A
Inequality 1 is incorrect; it should be g ≤ 80.
B
Inequality 1 is incorrect; it should be g ≥ 80.
C
Inequality 2 is incorrect; it should be g < 3k – 3.
D
Inequality 2 is incorrect; it should be g ≥ 3k – 3.
Explanation
“Not more than 80 years old” means the grandmother’s age can be 80 or less, so the correct inequality is g ≤ 80. The second inequality, g ≤ 3k − 3, correctly represents “at most 3 years less than 3 times” Kyle’s age. Therefore, Inequality 1 is incorrect; it should be g ≤ 80, which is choice A.
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