Which statements describe a combination of hours James can work mowing lawns and at the clothing store? Select TWO correct responses.

Steps to Solve

1. Define Variables

Let:

• $m$ = hours spent mowing lawns
• $c$ = hours spent working at the clothing store

2. Set Up Inequalities

From the problem, we know two things:

• Total hours worked should be less than 10: $$ m + c < 10 $$

• The total earnings should be at least $56. Assuming mowing lawns pays $8 per hour and working at the clothing store pays $12 per hour, we set up the equation: $$ 8m + 12c \geq 56 $$

3. Analyze Combinations

Now, we will analyze different combinations of $m$ and $c$ to find which meet both inequalities. We can start by trying various combinations that keep the total hours (m + c) under 10:

• For instance, if $m = 0$:

  • Then $c < 10$ and $12c \geq 56 \Rightarrow c \geq \frac{56}{12} \approx 4.67$. Hence, $c$ must be at least 5.

• If $m = 1$:

  • Then $c < 9$, so we calculate $8(1) + 12c \geq 56 \Rightarrow 12c \geq 48 \Rightarrow c \geq 4$ (c must be 4 or more).

Continue testing reasonable combinations of $m$ and $c$ until we find suitable values.

4. Final Verification

Ensure the chosen combination satisfies:

• $m + c < 10$
• $8m + 12c \geq 56$

5. List Compliant Combinations

Once you find combinations that fulfill both constraints, record them.