Question

Peyton is altering her new jacket to enter it into the Bodacious Bedazzling contest. In order for a garment to be considered "bedazzled," it must contain a number of gems that fall within the range of the following inequality

132≤7x≤193. Find the range of gems Peyton must use to enter her jacket into the contest.

Answer 1

The range of gems Peyton must use on her jacket to qualify for the Bedazzling contest is between 19 and 27 sets, which translates to between 133 and 189 gems, given the inequality 132≤7x≤193.

Step-by-step explanation:

Peyton is working on altering her new jacket to participate in the Bodacious Bedazzling contest. According to the inequality 132≤7x≤193, we need to determine the range of gems that Peyton must use. We will solve this inequality for x to find the minimum and maximum amount of gems.

First, we divide the entire inequality by 7:

• 132≤7 ≤ x ≤ 193≤7
• 18.857 ≤ x ≤ 27.571

Since the number of gems must be a whole number, we round the minimum number up and the maximum number down, thus the range for x becomes:

• 19 ≤ x ≤ 27

Therefore, Peyton must use between 19 and 27 sets of gems on her jacket to qualify for the contest, assuming one set includes 7 gems.