Sarah would like to make 5 lb. nut mixture that is 60% walnuts and 40% cashews. she has several pounds of walnuts and several pounds of a mixture that is 20% walnuts and 80% cashews. let w represent the number of pounds of walnuts needed to make the new mixture, and let m represent the number of pounds of the 80% cashew - 20% walnut mixture. a) write a system of linear equations that models this situation? b) which of the following is a solution to the system: 2 lb walnuts and 3 lb mixture or 2.5 lb walnuts and 2.5 lb mixture? show your work.

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.

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step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.