A nut wholesaler sell two types of mixes of cashews and peanuts. He makes low-grade mix containing 8 pound of peanuts and 4 pound of cashews and high-grade mixer containing 6 pound of peanuts and 6 pound of cashews. Let x and y denote the numbers of low-grade and high-grade packages that the wholesaler can make from 100 pound of peanuts and 80 pound of cashews. Which graph represents the possible combinations of packs of the two mixes that can be made?
What graphs? Cannot copy and paste here.
To find the possible combinations of packs of the two mixes that can be made, we need to set up a system of inequalities based on the given information.
Let's assume the wholesaler can make x packs of low-grade mix and y packs of high-grade mix.
From the information given, we know that each pack of low-grade mix contains 8 pounds of peanuts and 4 pounds of cashews, while each pack of high-grade mix contains 6 pounds of peanuts and 6 pounds of cashews.
Therefore, the total amount of peanuts used in the low-grade mix packs is 8x, and the total amount of peanuts used in the high-grade mix packs is 6y. Similarly, the total amount of cashews used in the low-grade mix packs is 4x, and the total amount of cashews used in the high-grade mix packs is 6y.
Based on these amounts, we can set up the following inequalities:
8x + 6y ≤ 100 (because the total weight of peanuts used should not exceed 100 pounds)
4x + 6y ≤ 80 (because the total weight of cashews used should not exceed 80 pounds)
To graph the solution to this system of inequalities, we first need to rearrange the equations:
8x + 6y ≤ 100 can be rewritten as y ≤ (-4/3)x + (50/3)
4x + 6y ≤ 80 can be rewritten as y ≤ (-2/3)x + (40/3)
Now we can plot the graphs of these inequalities on a coordinate plane:
Graph 1: y ≤ (-4/3)x + (50/3)
This is a line with a slope of -4/3 and a y-intercept of (0, 50/3).
Graph 2: y ≤ (-2/3)x + (40/3)
This is a line with a slope of -2/3 and a y-intercept of (0, 40/3).
The shaded region below both lines represents the possible combinations of packs of the two mixes that can be made.
Therefore, the graph that represents the possible combinations of packs of the two mixes is the shaded region below both Graph 1 and Graph 2.