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)

Answer 1

To represent the scenario with the variables given, we can write an equation based on the total amount Josie spends. The spending can be expressed as follows:

\[ 5x + 2y = 20 \]

where:
- \( x \) is the number of notebooks,
- \( y \) is the number of packs of pens.

To find a viable solution, we need to find integer values of \( x \) and \( y \) that satisfy this equation and also make sense in the context (i.e., both \( x \) and \( y \) should be non-negative).

Let's consider some possible integer solutions:

1. Set \( x = 0 \):
\[ 5(0) + 2y = 20 \]
\[ 2y = 20 \]
\[ y = 10 \]
(Solution: \( (0, 10) \))

2. Set \( x = 1 \):
\[ 5(1) + 2y = 20 \]
\[ 5 + 2y = 20 \]
\[ 2y = 15 \]
\[ y = 7.5 \]
(Not a viable solution since \( y \) must be an integer)

3. Set \( x = 2 \):
\[ 5(2) + 2y = 20 \]
\[ 10 + 2y = 20 \]
\[ 2y = 10 \]
\[ y = 5 \]
(Solution: \( (2, 5) \))

4. Set \( x = 3 \):
\[ 5(3) + 2y = 20 \]
\[ 15 + 2y = 20 \]
\[ 2y = 5 \]
\[ y = 2.5 \]
(Not a viable solution)

5. Set \( x = 4 \):
\[ 5(4) + 2y = 20 \]
\[ 20 + 2y = 20 \]
\[ 2y = 0 \]
\[ y = 0 \]
(Solution: \( (4, 0) \))

Collecting viable solutions, we have:
- \( (0, 10) \)
- \( (2, 5) \)
- \( (4, 0) \)

Any of these points represents a viable solution in the context of this scenario:
- \( (0, 10) \): 0 notebooks and 10 packs of pens.
- \( (2, 5) \): 2 notebooks and 5 packs of pens.
- \( (4, 0) \): 4 notebooks and 0 packs of pens.

Thus, several points can represent viable solutions. Please specify a point if you are looking for one specifically.