A nut wholesaler sells two types of mixes of cashews and peanuts. He makes a low grade mix containing 8 pounds of peanuts and 4 pounds of cashews and high-grade mixture containing 6 pounds of peanuts and 6 pounds of cashews. Let x and y denote the numbers of low-grade and high-grade packages that the wholesaler can make from 100 pounds of peanuts and 80 pounds of cashews. Represent the possible combinations of packs of the two mixes that can be made.
Answers
Answer:
Step-by-step explanation:
Given A nut wholesaler sells two types of mixes of cashews and peanuts. He makes a low grade mix containing 8 pounds of peanuts and 4 pounds of cashews and high-grade mixture containing 6 pounds of peanuts and 6 pounds of cashews. Let x and y denote the numbers of low-grade and high-grade packages that the wholesaler can make from 100 pounds of peanuts and 80 pounds of cashews.
If x represents packets for low grade nuts then mix of peanuts will be 8x and for low grade cashews the mix will be 4x
If y represents packets for high grade nuts then mix of peanuts will be 6y and for low grade cashews the mix will be 6y
So 8x + 6y <= 100
4x + 6y <=80
----------------------------
4x = 20
x = 5
8x + 6y = 100
8(5) + 6y = 100
40 + 6y = 100
6y = 100 - 40
6y = 60
y = 10
x < = 5 and y > = 10
x > = 10 and y < = 5
Put x = 1
8 + 6y < = 100
y < = 16
4 + 6y < = 80
y < = 12
With x = 1 and y < = 12
So these are cashews and peanuts which can be used.