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 ≤ 600 represents the possible combinations of pounds of hamburgers (x) and hot dogs (y) you can buy.
The graph shows a solid line with an x-intercept at 200, a y-intercept at 300, and shading below the line.
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
To test which of the given options is a solution to the inequality, we need to plug in the values of x and y from each option and check if the inequality holds true.
Option 1: 200 pounds of hamburgers and 140 pounds of hot dogs
3x + 2y = (3*200) + (2*140) = 840
But 840 is greater than 600, so this option is not a solution to the inequality.
Option 2: 150 pounds of hamburgers and 60 pounds of hot dogs
3x + 2y = (3*150) + (2*60) = 570
570 is less than or equal to 600, so this option is a solution to the inequality.
Option 3: 100 pounds of hamburgers and 240 pounds of hot dogs
3x + 2y = (3*100) + (2*240) = 780
780 is greater than 600, so this option is not a solution to the inequality.
Option 4: 240 pounds of hamburgers and 40 pounds of hot dogs
3x + 2y = (3*240) + (2*40) = 800
800 is greater than 600, so this option is not a solution to the inequality.
Therefore, the only option that represents a solution to the inequality is 150 pounds of hamburgers and 60 pounds of hot dogs.