Question

Josie spends $20 on school supplies. She purchases notebooks for $5 each and packs of pens for $2 each. Using x for notebooks and y for pens, which point represents a viable solution for this scenario?(1 point) Responses (2,5) left parenthesis 2 comma 5 right parenthesis (0.4,9) left parenthesis 0.4 comma 9 right parenthesis (8,−10) left parenthesis 8 comma negative 10 right parenthesis (3,2.5)

Answer 1

To determine which point represents a viable solution for Josie's purchases, we need to set up the equation based on her spending.

Let:
- \( x \) = number of notebooks
- \( y \) = number of packs of pens

The cost of notebooks is \( 5x \) (since each notebook costs $5) and the cost of pens is \( 2y \) (since each pack of pens costs $2). The total amount spent can be expressed by the equation:

\[ 5x + 2y = 20 \]

Now let's check each point to see if it satisfies this equation.

1. **Point (2, 5):**
\[
5(2) + 2(5) = 10 + 10 = 20 \quad \text{(valid solution)}
\]

2. **Point (0.4, 9):**
\[
5(0.4) + 2(9) = 2 + 18 = 20 \quad \text{(valid solution)}
\]

3. **Point (8, -10):**
\[
5(8) + 2(-10) = 40 - 20 = 20 \quad \text{(valid solution, but negative number of pens doesn’t make sense)}
\]

4. **Point (3, 2.5):**
\[
5(3) + 2(2.5) = 15 + 5 = 20 \quad \text{(valid solution, but cannot have half a pack of pens)}
\]

The only reasonable solutions based on real-world constraints (non-negative integers) for the number of notebooks and pens are point (2, 5).

Thus, the viable solution is **(2, 5)**.