Question

1. in order to participate in the alberta summer games, the track team had to have at least 12 members. write the inequality that represents this and give three possible solutions.

2 marks – 0.5 mark for the inequality and 0.5 mark for each solution

solve the inequality \\(\frac{c}{3} - \frac{1}{6} > \frac{5}{6}\\). show all steps.
5 marks – 1 mark for each step.

Explanation:

Problem 18 (Track Team Members)

Step1: Define variable and inequality

Let \( m \) be the number of team members. "At least 12" means \( m \geq 12 \).

Step2: Find possible solutions

We need values of \( m \) that satisfy \( m \geq 12 \). Three possible solutions:

• \( m = 12 \) (since 12 is at least 12)
• \( m = 13 \) (13 ≥ 12)
• \( m = 14 \) (14 ≥ 12)

Step1: Add \( \frac{1}{6} \) to both sides

To isolate the term with \( c \), add \( \frac{1}{6} \) to both sides:
\( \frac{c}{3} - \frac{1}{6} + \frac{1}{6} > \frac{5}{6} + \frac{1}{6} \)
Simplify: \( \frac{c}{3} > \frac{6}{6} \)
\( \frac{c}{3} > 1 \)

Step2: Multiply both sides by 3

To solve for \( c \), multiply both sides by 3 (since 3 is positive, the inequality sign remains):
\( 3 \times \frac{c}{3} > 1 \times 3 \)
Simplify: \( c > 3 \)

Answer:

Inequality: \( \boldsymbol{m \geq 12} \) (where \( m \) is the number of team members)
Possible solutions: \( 12 \), \( 13 \), \( 14 \) (other valid solutions like \( 15 \), \( 20 \), etc. are also acceptable)

Solve \( \frac{c}{3} - \frac{1}{6} > \frac{5}{6} \)