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) left parenthesis 3 comma 2.5 right parenthesis Skip to navigation page 12 of 12
Answers
GPT-4o mini
To determine which point represents a viable solution, we can set up the equation based on the total amount of money Josie spends on school supplies.
Let:
- \( x \) be the number of notebooks,
- \( y \) be the number of packs of pens.
The cost equation for the school supplies can be expressed as:
\[
5x + 2y = 20
\]
Now let's evaluate each option:
1. **(2,5)**:
\( 5(2) + 2(5) = 10 + 10 = 20 \) (valid solution)
2. **(0.4,9)**:
\( 5(0.4) + 2(9) = 2 + 18 = 20 \) (valid solution)
3. **(8,−10)**:
\( 5(8) + 2(-10) = 40 - 20 = 20 \) (not a valid solution because you cannot have a negative number of pens)
4. **(3,2.5)**:
\( 5(3) + 2(2.5) = 15 + 5 = 20 \) (not a valid solution because you cannot have half a pack of pens)
Based on the evaluations, the viable solutions from the options are (2, 5) and (0.4, 9).
However, if you need to choose just one point that is a valid solution, either (2, 5) or (0.4, 9) would work, but often, integer solutions (whole numbers) are favored in such scenarios.
Therefore, the point that best represents a viable solution is **(2, 5)**.
Let:
- \( x \) be the number of notebooks,
- \( y \) be the number of packs of pens.
The cost equation for the school supplies can be expressed as:
\[
5x + 2y = 20
\]
Now let's evaluate each option:
1. **(2,5)**:
\( 5(2) + 2(5) = 10 + 10 = 20 \) (valid solution)
2. **(0.4,9)**:
\( 5(0.4) + 2(9) = 2 + 18 = 20 \) (valid solution)
3. **(8,−10)**:
\( 5(8) + 2(-10) = 40 - 20 = 20 \) (not a valid solution because you cannot have a negative number of pens)
4. **(3,2.5)**:
\( 5(3) + 2(2.5) = 15 + 5 = 20 \) (not a valid solution because you cannot have half a pack of pens)
Based on the evaluations, the viable solutions from the options are (2, 5) and (0.4, 9).
However, if you need to choose just one point that is a valid solution, either (2, 5) or (0.4, 9) would work, but often, integer solutions (whole numbers) are favored in such scenarios.
Therefore, the point that best represents a viable solution is **(2, 5)**.