Question

Justin has collected 31 autographed football trading cards. The number of trading cards in Justin's

collection is fewer than twice the amount Jose has collected minus .
a. Write an inequality that can be used to find the number of cards Jose has collected.
b. What is the solution to the inequality?

Answer 1

Justin's collection of 31 autographed football cards is fewer than twice the number of cards Jose has minus one. We represent the number of Jose's cards with J and form the inequality 31 < 2J - 1. Solving this, we find that Jose has more than 16 cards.

Step-by-step explanation:

Inequality Representation

Let J represent the number of trading cards Jose has collected. According to the problem statement, Justin has 31 cards, which is fewer than twice the amount that Jose has, minus one. Therefore, the inequality can be written as:

31 < 2J - 1

Solving the Inequality

To find how many cards Jose has, we need to solve the inequality for J:

1. Add 1 to both sides of the inequality to isolate the term with J: 31 + 1 < 2J
2. Simplify: 32 < 2J
3. Divide both sides by 2 to solve for J: 32 / 2 < J
4. J > 16

Thus, Jose has collected more than 16 cards.