Question

Tamlin is learning to become a carpenter. She gets paid $12 per hour for building shelves and $14 per hour for building cabinets. She can work a maximum of 40 hours per week, and she would like to earn at least $250 this week. Lets represent the number of hours she spends building shelves and c represent the number of hours she spends building cabinets. Which system of inequalities could be used to represent the given conditions?

Answer 1

Tamlin's work conditions can be represented by a system of inequalities using 's' for hours building shelves and 'c' for cabinets. The inequalities are s + c ≤ 40 and 12s + 14c ≥ 250, which account for her weekly working hours limit and her desired minimum earnings.

Step-by-step explanation:

To represent Tamlin’s work conditions and earnings as a system of inequalities, we need to define the variables as such:

• s represents the number of hours spent building shelves.
• c represents the number of hours spent building cabinets.

Based on the question, the following system of inequalities can be formulated:

1. s + c ≤ 40 (Tamlin can work a maximum of 40 hours per week.)
2. 12s + 14c ≥ 250 (She wants to earn at least $250 this week, earning $12 per hour for shelves and $14 per hour for cabinets.)

This system reflects both the constraints on her time and the minimum income requirement.

Answer 2

`\begin{gathered} \text{The system of inequalities must be then} \\ s+c\ge40 \\ 12s+14c\ge250 \end{gathered}`