You can use trial and error for 3 drinks and 2 drinks and can see how many hot dogs are available for Jacob to buy in $18 budget.
Jacob, with $18 dollars for food, under given conditions, can buy:
Option D: 2 drinks and 5 hot dogs.
How to decide what amount of drinks and hot dogs are obtainable in given $18 budget?
This can be modeled by mathematical expression with use of variables, and inequality.
Suppose that you can by [tex]x[/tex] drinks and [tex]y[/tex] hot dogs, then their amount should not exceed $18 and they should try to use that $18 as much as they can.
Since 1 drink costs $1.5 and 1 hot dog costs $2.75, thus,
[tex]1.5x + 2.75y \leq18[/tex]
Using trial and error for 2 and 3 drinks (we could've done fro 5 or 7 hot dogs too)
For 2 drinks:
Since x = amount of drinks = 2, thus from the obtained inequality, we have:
[tex]1.5x + 2.75y \leq 18\\1.5 \times 2 + 2.75y \leq 18\\2.75y \leq 18 - 3\\y \leq \dfrac{15}{2.75}\\\\y \leq 5.555...\\y = 5[/tex]
We took y = 5 since it is closest integer less than 5.55... since we cannot buy drink or hot dog in decimal points generally and cannot spend more than $18
Thus, if Jacob buys 2 drinks, then he can by 5 hot dogs at max.
For 3 drinks:
Since drinks' amount increased, then hot dogs amount will have to decrease to keep them together under $18. And since in 2 drinks Jacob could by 5 hot dogs, thus, now he will have to buy less than 5 hot dogs, which are not given in options.
Thus,
Jacob, with $18 dollars for food, under given conditions, can buy:
Option D: 2 drinks and 5 hot dogs.
Learn more about inequalities here:
https://brainly.com/question/11901702
