Algebra unit test 6 A community.

Question

Center is running a special program for arts and crafts classes.The center can accommodate a maximum of 150 participants.The center is offering two types of classes painting(P) And pottery(T). Each painting class requires Three participants to run while each pottery class requires five participants
1. Create a two veritable linear That represents the constraint of total.Number of participants clearly define your variables (five points)
2. The center schedules ten painting classes and five pottery classes usinginequality Created in part 1, determine if this schedule meets the participants capacity. (2 points)

Answer 1

Let's tackle the problem step by step.

1. Define Variables and Create Inequality

Define the Variables:

• Let \( P \) be the number of painting classes.
• Let \( T \) be the number of pottery classes.

Creating the Inequality: Each painting class requires 3 participants, and each pottery class requires 5 participants. The maximum number of participants allowed is 150.

The constraint can be represented in inequality form as follows:

\[ 3P + 5T \leq 150 \]

2. Check the Scheduled Classes Against the Capacity

Now, we have the center scheduling 10 painting classes and 5 pottery classes.

Substituting the values into the equation:

• \( P = 10 \)
• \( T = 5 \)

Substituting these values into the inequality:

\[ 3(10) + 5(5) \leq 150 \] \[ 30 + 25 \leq 150 \] \[ 55 \leq 150 \]

Conclusion

Since the result \( 55 \leq 150 \) is true, this means that the schedule of 10 painting classes and 5 pottery classes does meet the participant capacity limitation.