Question

1. kyra and five friends shared a bag of fruit snacks. each person got no more than 3 fruit snacks. the inequality ( x div 6 leq 3 ) represents this situation. solve the inequality to find the possible numbers of fruit snacks that were in the bag.
2. over the next 17 months, eli needs to read more than 102 e - books. the inequality ( 17x > 102 ) represents the number of e - books he needs to read per month. solve the inequality to find the number of e - books eli needs to read per month.

Explanation:

Problem 10 (Kyra and fruit snacks)

Step1: Identify the inequality

The inequality given is \( \frac{x}{6} \leq 3 \), where \( x \) is the number of fruit snacks.

Step2: Solve the inequality

To solve for \( x \), multiply both sides of the inequality by 6.

$$ \frac{x}{6} \times 6 \leq 3 \times 6 $$

Simplifying both sides, we get:

$$ x \leq 18 $$

Also, since the number of fruit snacks can't be negative, \( x \geq 0 \). But in the context of sharing, \( x \) should be a non - negative integer, and from the inequality solution, \( x \leq 18 \).

Step1: Identify the inequality

The inequality given is \( 17x>102 \), where \( x \) is the number of e - books Eli reads per month.

Step2: Solve the inequality

To solve for \( x \), divide both sides of the inequality by 17.

$$ \frac{17x}{17}>\frac{102}{17} $$

Simplifying both sides, we get:

$$ x > 6 $$

Answer:

The possible number of fruit snacks \( x \) satisfies \( 0\leq x\leq18 \) (where \( x \) is a non - negative integer, and in the context of the problem, \( x \) represents the number of fruit snacks, so \( x \) can be 0, 1, 2, \(\cdots\), 18). If we consider the practical situation of having at least 1 snack (since they are sharing a bag of snacks), \( 1\leq x\leq18 \) with \( x\in\mathbb{Z}\). But from the inequality solution alone, \( x\leq18 \) and \( x\geq0 \).

Problem 11 (Eli and e - books)