Answer:
Cost for each pound of chocolate chips = $3.00
Cost for each pound of walnuts = $1.50
Explanation:
We can determine the cost for each pound of chocolate chips and each pound of walnuts using a system of equations, where:
- c refers to the cost of each pound of chocolate chips,
- and w refers to the cost of each pound of walnuts.
First equation:
We know that the cost for 3 pounds of chocolate chips and 8 pounds of walnuts equals the total cost:
(pounds * cost of chocolate chips) + (pounds * cost of walnuts) = total cost
Since the total cost for 3 pounds of chocolate chips and 8 pounds of walnuts is $21, our first equation is given by:
3c + 8w = 21
Second equation:
We know that the cost for 5 pounds of chocolate chips and 2 pounds of walnuts equals the total cost:
(pounds * cost of chocolate chips) + (pounds * cost of walnuts) = total cost
Since the total cost for 5 pounds of chocolate chips and 2 pounds of walnuts is $18, our second equation is given by:
5c + 2w = 18
Method to solve: Elimination:
Before we begin solving, we can multiply the second equation by -4, which will allow us to eliminate the ws since 8w - 8w = 0:
-4(5c + 2w = 18)
-20c - 8w = -72
Solving for c (the cost for each pound of chocolate chips):
Now we can solve for c (the cost for each pound of chocolate chips) by adding the first equation and the second equation:
3c + 8w = 21
+
-20c - 8w = -72
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(3c - 20c) + (8w - 8w) = (21 - 72)
(-17c = -51) / -17
c = 3
Thus, the cost for each pound of chocolate chips is $3.00.
Solving for w (the cost for each pound of walnuts):
Now we can solve for w (the cost for each pound of walnuts) by plugging in 3 for c in the first equation (3c + 8w = 21):
3(3) + 8w = 21
(9 + 8w = 21) - 9
(8w = 12) / 8
w = 1.5
Thus, the cost for each pound of walnuts is $1.50.