Question

I want to mix peach candy worth $2.80 per pound and lemon candy worth $3.20 per pound to create a 20-pound mixture worth $3.00 per pound. Can you help me find a similar problem on the website to determine how many pounds of each type of candy I should use?

Answer 1

Certainly! To determine the amount of each type of candy needed for your mixture, we can set up a system of equations based on the information provided.

Let:
- \( x \) = pounds of peach candy
- \( y \) = pounds of lemon candy

From the problem, we have two equations:

1. The total weight of the mixture:
\[
x + y = 20
\]

2. The total value of the mixture:
\[
2.80x + 3.20y = 3.00 \times 20
\]

Now let's simplify the second equation:
\[
2.80x + 3.20y = 60
\]

Now you can solve these equations step by step.

First, solve for \( y \) in terms of \( x \) in the first equation:
\[
y = 20 - x
\]

Substitute \( y \) in the second equation:
\[
2.80x + 3.20(20 - x) = 60
\]

Now expand and simplify:
\[
2.80x + 64 - 3.20x = 60
\]
Combine like terms:
\[
-0.40x + 64 = 60
\]
Rearranging gives:
\[
-0.40x = 60 - 64
\]
\[
-0.40x = -4
\]
\[
x = \frac{-4}{-0.40} = 10
\]

Now substitute \( x = 10 \) back into the first equation to find \( y \):
\[
y = 20 - 10 = 10
\]

Thus, you should use **10 pounds of peach candy** and **10 pounds of lemon candy** to create a 20-pound mixture worth $3.00 per pound.

If you're looking for similar problems, you can generally find them under sections dealing with word problems or systems of equations in algebra textbooks or online resources. Search for problems involving mixtures or "blending problems" as they often cover similar concepts.