Answer:
To solve this problem, we can use a system of equations.
Let's say the number of pounds of raisins that Amy uses is "x," and the number of pounds of nuts she uses is "y."
According to the given information, the price of raisins per pound is $1.60, and the price of nuts per pound is $2.45.
Since Amy wants to make a mixture worth $2 per pound, we can create the following equation for the total value of the mixture:
1.60x + 2.45y = 2 * 17
Simplifying the equation, we have:
1.60x + 2.45y = 34
Now, we need to account for the total weight of the mixture, which is 17 pounds:
x + y = 17
To solve this system of equations, we can use substitution or elimination.
Let's solve it using the elimination method:
Multiply the second equation by 1.60 to make the coefficients of "x" in both equations equal:
1.60(x + y) = 1.60(17)
1.60x + 1.60y = 27.2
Now, we have two equations:
1.60x + 2.45y = 34
1.60x + 1.60y = 27.2
Subtract the second equation from the first to eliminate "x":
(1.60x + 2.45y) - (1.60x + 1.60y) = 34 - 27.2
0.85y = 6.8
Divide both sides of the equation by 0.85 to solve for "y":
y = 6.8 / 0.85
y = 8
Now, substitute the value of "y" into one of the original equations (let's use the second equation):
x + 8 = 17
Subtract 8 from both sides of the equation to solve for "x":
x = 17 - 8
x = 9
So, Amy should use 9 pounds of raisins and 8 pounds of nuts to make a 17-pound mixture worth $2 per pound.
Explanation: