Question

You are serving bratwurst and hamburgers at your annual picnic. You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.

Let x be the number of bratwursts and y the number of hamburgers. whiichs system of inequalities represents this situation?

Options:
x+y<=40 1.35x+1.2y>=175
x+y<=40 1.35x+1.2y<=175
x+y>=120 1.35x+1.2>=175
x+y>=120 1.35x+1.2<=175
...?

Answer 1

Option D -
`x+y\geq 120` ,
`1.35x + 1.2y \leq 175`

Explanation:

Given : You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.

To find : Which system of inequalities represents this situation?

Solution :

Let x be the number of bratwursts and y the number of hamburgers.

You want at least three bratwursts or hamburgers for each of your 40 guests.

i.e, you want at least
`3*(40)=120` bratwursts or hamburgers.

We can write the equation as,

Number of bratwursts + number of hamburgers at least 120

`x+y\geq 120`

Bratwursts cost $1.35 each and hamburgers cost $1.2 each. Your budget is $175.

We can write equations as ,

Cost of bratwursts + cost of hamburgers at most 175

`1.35x + 1.2y \leq 175`

Therefore, The system of linear equation form is
`x+y\geq 120`,
`1.35x + 1.2y \leq 175`

Hence, Option D is correct.

Answer 2

x+y>=120 1.35x+1.2<=175

Is the logical interpretation of this scenario.