Question

The non-profit organization you volunteer for is throwing a fundraiser cookout. You are in charge of buying the hamburgers, which cost $3 per pound, and hot dogs, which cost $2 per pound. The meat budget you are given totals $600 dollars. The inequality 3x + 2y less than or equal to 600 represents the possible combinations of pounds of hamburgers (x) and hot dogs (y) you can buy.

Answer 1

`150` pounds of hamburgers and
`60` pounds of hot dogs

Explanation:

The options are

Which of the following represents a solution to the inequality?

`200` pounds of hamburgers and
`140` pounds of hot dogs

`150` pounds of hamburgers and
`60` pounds of hot dogs

`100` pounds of hamburgers and
`240` pounds of hot dogs

`240` pounds of hamburgers and
`40` pounds of hot dogs

Let

x------> the pounds of hamburgers

y------> the pounds of of hot dogs

we know that

The inequality that represent the situation is equal to

`3x+2y\leq 600`

Remember that

If a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

Verify each case

case A)
`200` pounds of hamburgers and
`140` pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

`3(200)+2(140)\leq 600`

`880\leq 600` ------> is not true

therefore

the case A) is not a solution

case B)
`150` pounds of hamburgers and
`60` pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

`3(150)+2(60)\leq 600`

`570\leq 600` ------> is true

therefore

the case B) is a solution

case C)
`100` pounds of hamburgers and
`240` pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

`3(100)+2(240)\leq 600`

`780\leq 600` ------> is not true

therefore

the case C) is not a solution

case D)
`240` pounds of hamburgers and
`40` pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

`3(240)+2(40)\leq 600`

`800\leq 600` ------> is not true

therefore

the case D) is not a solution

Answer 2

Which of the following represents a solution to the inequality?
200 pounds of hamburgers and 140 pounds of hot dogs
150 pounds of hamburgers and 60 pounds of hot dogs
100 pounds of hamburgers and 240 pounds of hot dogs
240 pounds of hamburgers and 40 pounds of hot dogs

x = hamburger ; y = hot dog
3x + 2x < 600

3(200) + 2(140) = 600 + 280 = 880 No.
3(150) + 2(60) = 450 + 120 = 570 YES.
3(100) + 2(240) = 300 + 480 = 780 No.
3(240) + 2(40) = 720 + 80 = 800 No.

150 pounds of hamburgers and 60 pounds of hot dogs