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:

The correct option is :

Inequality 1 is incorrect; it should be g ≤ 80.

Step-by-step explanation:

Let Kyle's age be = k

Let the grandmother's age be = g

Kyle says his grandmother is not more than 80 years old. This means $g\leq 80$

He says his grandmother’s age is, at most, 3 years less than 3 times his own age. This means $g\leq 3k-3$

Jane wrote:

Inequality 1: $g>80$

Inequality 2: $g\leq 3k- 3$

Jane wrote the 1st inequality wrong. As she has shown that the grandmother's age is greater than 80, which is not.

So, the correct option is :

Inequality 1 is incorrect; it should be g ≤ 80.