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Answer:
a) w+c = 5 ____equation(1) and w = c ____equation (2)
b) 2.5 lb walnuts and 2.5 lb cashews
Step-by-step explanation:
Let w pounds be the weight of walnuts required and c pounds be the weight of cashews required to make the new mixture.
Total weight of the new mixture = 5 lb
So,
Weight of walnuts + Weight of cashews = Total weight of the new mixture
w+c = 5 ____equation (1)
Now,
60% of walnuts +40% of cashews = 20% of walnuts + 80% of cashews
0.60w+0.40c = 0.20w+0.80c
Subtracting 0.20w from both the sides of the equation, we get
0.60w+0.40c-0.20w = 0.20w+0.80c-0.20w
Cancelling out the 0.20w and -0.20w from the right side, we have
0.60w-0.20w+0.40c = 0.80c
=> 0.40w+0.40c=0.80c
Subtracting 0.40c from both sides, we get
0.40w+0.40c-0.40c=0.80c-0.40c
Cancelling out 0.40c and -0.40 c form the left side, we get
0.40w = 0.40c
Dividing both sides by 0.40, we have
Cancelling out the 0.40's from the top and bottom, we get
w = c ____equation (2)
Plugging in w=c into the equation 1, we get
w+c = 5
=> c+c =5
=> 2c = 5
Dividing both sides by 2, we get
Cancelling out the 2's from the left, we get
c = 2.5
Plugging in c=2.5 into the equation 1, we get
w+c = 5
=> w + 2.5 = 5
Subtracting 2.5 from both sides, we get
w+ 2.5 -2.5 = 5 - 2.5
Cancelling out the +2.5 and -2.5 from the left side, we get
w = 2.5
So, we need 2.5 lb walnuts and 2.5 lb cashews to make the new mixture.