Answer: amount of nuts = 2 pounds amount of dried fruit = 4 pounds
Explanation: We are given that x is the amount of nuts and y is the amount of dried fruit. We are also given that: 1- Hunter needs to make 6 pounds of trail mix. This means that: x + y = 6 This can be rewritten as: x = 6 - y .........> equation I 2- x costs $4 per pound, y costs $3.5 and Hunter can spend a total of $22. This means that: 4x + 3.5y = 22 ..........> equation II
Substitute with equation I in equation II and solve for y as follows: 4x + 3.5y = 22 4(6-y) + 3.5y = 22 24 - 4y + 3.5y = 22 24-22 = 4y-3.5y 2 = 0.5y y = 4 pounds
Substitute with y in equation I to get the value of x as follows: x = 6-y x = 6-4 x = 2 pounds
<em>The linear equations have the same slope, so the rate of change for each is the same. As long as the rate of change is the same, the lines will stay the same distance apart and not intersect.</em>
