Question

The owner of a grocery store wants to mix two kinds of candy together to make 15 lb that he can sell for $5 per lb. He wants to use chocolate candies that he sells for $7 per lb and sugar candies that he sells for $2 per lb. How many pounds of each should the owner use?

Answer 1

To create a candy mix selling for $5 per lb from $7 per lb chocolate and $2 per lb sugar candies, equations based on total weight (x + y = 15) and cost (7x + 2y = 75) are solved, revealing 5 lbs of chocolate and 10 lbs of sugar candies are needed.

To solve the problem of mixing candies to achieve a certain price per pound, we can use a system of linear equations. Let x be the pounds of chocolate candies and y be the pounds of sugar candies. The chocolate candies cost $7 per lb (x), and the sugar candies cost $2 per lb (y), with a desired mix of 15 lb that sells for $5 per lb.

1. Formulate the first equation based on the total weight: x + y = 15.
2. Formulate the second equation based on the total cost: 7x + 2y = 15 * 5.
3. Solve the system of equations using substitution or elimination.

By solving the equations, we find that the store owner should use 5 lbs of chocolate candies and 10 lbs of sugar candies to achieve the desired mixture.