To determine which situation cannot be modeled by the equation [tex]\(5x - 15y = 335\)[/tex], let’s analyze each option:
### Option A:
Randy earns [tex]\(\$5\)[/tex] for each hour he works and spends [tex]\(\$15\)[/tex] each time he goes out to dinner. He has [tex]\(\$335\)[/tex] at the end of the week.
Let:
- [tex]\(x\)[/tex] be the number of hours Randy works.
- [tex]\(y\)[/tex] be the number of times Randy goes out to dinner.
The equation modeling his earnings and expenditures would be:
[tex]\[ 5x - 15y = 335 \][/tex]
So, Option A can be modeled by the equation.
### Option B:
A hamburger sells for [tex]\(\$5\)[/tex] but costs [tex]\(\$0.15\)[/tex] to make, giving a net income of [tex]\(\$3.35\)[/tex].
Let:
- [tex]\(x\)[/tex] be the number of hamburgers sold.
The net income per hamburger would be:
[tex]\[ 5 - 0.15 = 4.85 \][/tex]
If we multiply the number of hamburgers [tex]\(x\)[/tex] by this net income, the total income would be:
[tex]\[ 4.85x \][/tex]
However, we need the net income (total income minus total cost) to equal [tex]\(\$3.35\)[/tex]:
[tex]\[ 4.85x = 3.35 \][/tex]
This does not align with the equation [tex]\(5x - 15y = 335\)[/tex], since there's no [tex]\(y\)[/tex] involved or a clear way to adapt the situation to fit the format. So, Option B cannot be modeled by the equation.
### Option C:
Ruby is paid for the 5 sales she made but docked for the 15 sales she missed for a net income of \$335.
Let:
- [tex]\(x\)[/tex] be the number of sales made.
- [tex]\(y\)[/tex] be the number of sales missed.
The equation modeling this would be:
[tex]\[ 5x - 15y = 335 \][/tex]
So, Option C can be modeled by the equation.
### Option D:
Tommy earned points for 5 correct answers on a standardized test but was docked for 15 incorrect answers for a point total of 335.
Let:
- [tex]\(x\)[/tex] be the number of correct answers.
- [tex]\(y\)[/tex] be the number of incorrect answers.
The equation modeling this would be:
[tex]\[ 5x - 15y = 335 \][/tex]
So, Option D can be modeled by the equation.
### Conclusion:
The situation that cannot be modeled by the equation [tex]\(5x - 15y = 335\)[/tex] is Option B.
