Answer:the number of $2.89 per pound nut that is put in the mixture is 29
the number of $4.29 per pound nut that is put in the mixture is 21
Explanation:
Let x represent the number of $2.89 per pound nut that should be put in the mixture.
Let y represent the number of $4.29 per pound nut that should be put in the mixture.
A grocer mixes 2 kinds of nuts that cost to $2.89 and for $4.29 per pound to make 50 pounds of a mixture. This means that
x + y = 50
The mixture costs $3.49 per pound. This means that the 50 pounds mixture would cost 50 × 3.49 = 174.5
Therefore, the total cost of the mixture made by the grocer would be
2.89x + 4.29y = 174.5 - - - - - - - - -1
Substituting x = 50 - y into equation 1, it becomes
2.89(50 - y) + 4.29y = 174.5
144.5 - 2.89y + 4.29y = 174.5
- 2.89y + 4.29y = 174.5 - 144.5
1.4y = 30
y = 30/1.4 = 21
Substituting y = 21 into x = 50 - y, it becomes
x = 50 - 21 = 29