Answer: 2.4 pounds of the type of nut that sells for $3.00/lb and 4.8 pounds of the type of nut that sells for $5.40/lb would be needed.
Step-by-step explanation:
Let x represent the number of pounds of the type of nut that sells for $3.00/lb that you would need.
Let y represent the number of pounds of the type of nut that sells for $5.40/lb that you would need.
You would like to have 7.2 lbs of a nut mixture. It means that
x + y = 7.2
The mixture would sell for $4.60/lb. It means that the cost of the mixture would be
4.6 × 7.2 = $33.12
This means that
3x + 5.4y = 33.12- - - - - - - - - 1
Substituting x = 7.2 - y Intl equation 1, it becomes
3(7.2 - y) + 5.4y = 33.12
21.6 - 3y + 5.4y = 33.12
- 3y + 5.4y = 33.12 - 21.6
2.4y = 11.52
y = 11.52/2.4
y = 4.8
x = 7.2 - y = 7.2 - 4.8
x = 2.4
