I need help with a mixture problem

Question

Macario is making 11 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $8.15$ per pound and almonds cost $5.1$ per pound. How many pounds of macadamia nuts and how many pounds of almonds should Macario use for the mixture to cost $6.07 per pound to make? Round your answer to one decimal place, if necessary. I am having trouble solving this problem if anyone can help me and explain to me how to do the problem I would appreciate it

Answer 1

8.15M + 5.1A = 6.07B

where M= pounds of Macadamia nuts, A = pounds of almonds and B = pounds of the mixture = 11

8.15M + 5.1(11-M) = 6.07(11) = 66.77

8.15M -5.1M = 66.77-5.1(11) = 10.67

M = 10.67/3.05 = about 3.5 pounds of Macadamia nuts, costing $8.15 per pound

11-3.5 = 7.5 pounds of Almonds costing $5.10 per pound

to get 11 pounds of a mixture costing $6.07 per pound

8.15(3.5) + 5.1(7.5)= about 28.5 + 38.3 = 64.8

6.07(11) = 66.7

notice from the start, 6.07 is closer to 5.1 than to 8.15 so you'll need more of the 5.1

6.07 is within .97 of 5.1

8.15 is within 2.08 of 5.1.

2.08 is about but a little over 2 times .97

so you'll need about but a little over two times as many Almonds

7.5/3.5 = about 2.14

2.08/,97 = about 2.14