Question

You have one type of candy that sells for $1.90/lb and another type of candy that sells for $9.80/lb. You would like to have 55.3 lbs of a candy mixture that sells for $5.30/lb. How much of each candy will you need to obtain the desired mixture?

A. 23.5 lbs of $1.90/lb candy and 31.8 lbs of $9.80/lb candy
B. 31.8 lbs of $1.90/lb candy and 23.5 lbs of $9.80/lb candy
C. 24.5 lbs of $1.90/lb candy and 30.8 lbs of $9.80/lb candy
D. 30.8 lbs of $1.90/lb candy and 24.5 lbs of $9.80/lb candy

Answer 1

To create a candy mixture selling for $5.30/lb, 31.8 lbs of $1.90/lb candy and 23.5 lbs of $9.80/lb candy are needed. The calculation involves solving a system of equations representing the weight and cost of the mixture.

Step-by-step explanation:

To solve the problem of creating a mixture of candies that sells for $5.30 per lb, we need to find the correct ratio of two types of candy, one selling at $1.90 per lb and the other selling at $9.80 per lb.

Let's define x as the weight of the $1.90/lb candy and y as the weight of the $9.80/lb candy needed for the mixture. We have two equations: the weight equation and the cost equation.

1. The weight equation: x + y = 55.3 lbs
2. The cost equation: 1.90x + 9.80y = 5.30 * 55.3

We will solve this system of equations to find the weights of each candy type required for the mix.

First, multiply the total weight by the desired price per pound to find the total cost of the mixture:

Total cost = 55.3 lbs * $5.30/lb = $293.09

Now, use this total cost in the cost equation:

1.90x + 9.80y = $293.09

Substituting the weight equation into the cost equation gives:

1.90x + 9.80(55.3 - x) = $293.09

After solving this equation for x, we find that:

x = 31.8 lbs and therefore y = 55.3 lbs - 31.8 lbs = 23.5 lbs.

Thus, the correct mixture requires 31.8 lbs of $1.90/lb candy and 23.5 lbs of $9.80/lb candy, which corresponds to option B.