You have one type of nut that sells for $4.50/lb and another type of nut that sells for $8.80/lb. You would like to have 12.9 lbs of a nut mixture that sells for $8.00/lb. How much of each nut will you need to obtain the desired mixture?

The quantity of first nut = x = 2.4 lb

The quantity of second nut = 12.9 - x = 12.9 - 2.4 = 10.5 lb

Step-by-step explanation:

Let amount of first type of nut = x

Amount of second type of nut = 12.9 - x

Total Cost of  first type of nut = 4.5 x

Total Cost of second type of nut = 8.8 × (12.9 -  x)

Total cost of both type of nut = 8 × 12.9

Total cost = Cost of first type of nut + Cost of second type of nut

8 × 12.9 = 4.5 x + 8.8 × (12.9 -  x)

103.2 = 4.5 x + 113.52 - 8.8 x

8.8 x - 4.5 x = 10.32

4.3 x = 10.32

x = 2.4

Therefore the quantity of first nut = x = 2.4 lb

The quantity of second nut = 12.9 - x = 12.9 - 2.4 = 10.5 lb