Answer: 37 kilograms of walnuts should be mixed.
Step-by-step explanation:
Let x represent the number of kilograms of peanuts needed to make the mixture.
Let y represent the number of kilograms of walnut needed to make the mixture.
The mixture to be made is 100 kg. It means that
x + y = 100
The worth of the mixture is $3.24 per kilogram. It means that the total worth of the mixture is
3.24 × 100 = $324
peanuts cost $2.50 per kilogram and walnuts cost $4.50 per kilogram. It means that
2.5x + 4.5y = 324- - - - - - - - - -1
Substituting x = 100 - y into equation 1, it becomes
2.5(100 - y) + 4.5y = 324
250 - 2.5y + 4.5y = 324
- 2.5y + 4.5y = 324 - 250
2y = 74
y = 74/2 = 37
x = 100 - y = 100 - 37
x = 63
