Candy worth $2.45 per pound is mixed with candy worth $2.30 per pound.How much of each kind of candy must be used to have 30 pounds of a mixture worth $2.35 per pound?

X lbs @ $2.45/lb.

(30-X)lbs @ $2.30/lb.

2.45X + 2.30(30 - X) = $2.35*30,
2.45X + 69 - 2.30X = 70.5,
0.15X = 70.5 - 69 = 1.5,
X = 10lbs. @ $2.45/lb.

30 - X = 30 - 10 = 20lbs @ $2.30/lb.

To solve this problem, we can use the method of solving systems of equations. Let's assume that the amount of candy worth $2.45 per pound is x pounds, and the amount of candy worth $2.30 per pound is y pounds.

Since we have 30 pounds of mixture, we can write the following equation for the total weight:
x + y = 30 Equation 1

Also, the value of the mixture (cost per pound) can be calculated by multiplying the weight of each type of candy by its respective price per pound and dividing by the total weight:
(2.45x + 2.30y)/30 = 2.35 Equation 2

To solve this system of equations, we can use the substitution method or the elimination method. In this case, let's use the elimination method.

First, let's multiply both sides of Equation 2 by 30 to remove the denominator:
2.45x + 2.30y = 2.35 * 30
2.45x + 2.30y = 70.5 Equation 3

Now, let's multiply both sides of Equation 1 by 2.30 to make the coefficients of y the same in both equations:
2.30x + 2.30y = 2.30 * 30
2.30x + 2.30y = 69 Equation 4

By subtracting Equation 4 from Equation 3, we can eliminate the y term:
(2.45x - 2.30x) + (2.30y - 2.30y) = 70.5 - 69
0.15x = 1.5

Dividing both sides of this equation by 0.15 will give us the value of x:
x = 1.5 / 0.15
x = 10

Now, substituting the value of x into Equation 1, we can solve for y:
10 + y = 30
y = 30 - 10
y = 20

Therefore, the amount of candy worth $2.45 per pound that must be used is 10 pounds, and the amount of candy worth $2.30 per pound is 20 pounds.

Let's break down the problem step by step.

Let's assume that x pounds of candy worth $2.45 per pound is mixed with y pounds of candy worth $2.30 per pound. We are given that we want to have a total of 30 pounds of the mixture and that the final mixture should be worth $2.35 per pound.

First, let's set up the equation for the total weight of the mixture:

x + y = 30

Next, let's set up the equation for the total value of the mixture:

(2.45 * x) + (2.30 * y) = 2.35 * 30

Now, we have a system of two equations:

x + y = 30 -> Equation 1
(2.45 * x) + (2.30 * y) = 2.35 * 30 -> Equation 2

To solve this system, we can use the substitution method or the elimination method. Let's solve it using the substitution method.

Solving Equation 1 for x:

x = 30 - y

Substituting the value of x in Equation 2:

(2.45 * (30 - y)) + (2.30 * y) = 2.35 * 30

Simplifying the equation:

73.5 - 2.45y + 2.30y = 70.5

Combine like terms:

-0.15y = -3

Divide both sides by -0.15:

y = 20

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

x + 20 = 30
x = 10

Therefore, you need 10 pounds of candy worth $2.45 per pound and 20 pounds of candy worth $2.30 per pound to have a 30-pound mixture worth $2.35 per pound.