Answer:
To determine how many pounds of each type of candy you bought, let's set up a system of equations based on the given information.
Let's assume you bought x pounds of Candy A and y pounds of Candy B.
According to the given information, the cost of Candy A is $4.20 per pound, so the cost of x pounds of Candy A would be 4.20x dollars.
Similarly, the cost of Candy B is $5.65 per pound, so the cost of y pounds of Candy B would be 5.65y dollars.
Since the total cost of the candy is $64.60, we can set up the equation:
4.20x + 5.65y = 64.60
Additionally, we know that the total weight of candy purchased is 14 pounds, so we have the equation:
x + y = 14
Now we have a system of two equations:
4.20x + 5.65y = 64.60
x + y = 14
To solve this system, we can use substitution or elimination methods.
Let's use the elimination method. Multiply the second equation by 4.20 to eliminate the x term:
4.20(x + y) = 4.20(14)
4.20x + 4.20y = 58.80
Now we have the following system of equations:
4.20x + 5.65y = 64.60
4.20x + 4.20y = 58.80
Subtract the second equation from the first equation:
(4.20x + 5.65y) - (4.20x + 4.20y) = 64.60 - 58.80
1.45y = 5.80
Divide both sides by 1.45 to solve for y:
y = 5.80 / 1.45
y = 4
Substitute the value of y back into the second equation to solve for x:
x + 4 = 14
x = 14 - 4
x = 10
Therefore, you bought 10 pounds of Candy A and 4 pounds of Candy B to stay within your budget of $64.60 and purchase a total of 14 pounds of candy.
Explanation: