Question

Please Help.

Hunter needs to make trail mix with nuts and dried fruit. The nuts cost $4 per pound and the dried fruit costs $3.50 per pound. Hunter can spend a total of $22 and he needs to make six pounds of trail mix.

Let x = the amount of nuts.

Let y = the amount of dried fruit.

How many pounds of dried fruit can Hunter purchase?

Answer 1

Answer:
amount of nuts = 2 pounds
amount of dried fruit = 4 pounds

Step-by-step 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

Hope this helps :)