Question

A certain brand of razor blades in packages of 6, 12, and 24 blades, costing $3, $4, and $5 per package, respectively. A store sold 12 packages containing a total of 258 razor blades and took in $73. How many packages of each type were sold?

a) 2 packages of 6 blades, 6 packages of 12 blades, 4 packages of 24 blades
b) 6 packages of 6 blades, 4 packages of 12 blades, 2 packages of 24 blades
c) 4 packages of 6 blades, 6 packages of 12 blades, 2 packages of 24 blades
d) 3 packages of 6 blades, 5 packages of 12 blades, 4 packages of 24 blades

Answer 1

To find out how many packages of razor blades were sold, a system of equations is created and solved. The calculations reveal that the store sold 6 packages of 6 blades, 4 packages of 12 blades, and 2 packages of 24 blades.

Step-by-step explanation:

The student's question involves solving a problem using systems of equations, where razor blades are sold in different package sizes with corresponding prices, and we need to figure out how many packages of each type were sold given the total number of blades and the total revenue.

To solve this problem, we need to set up a system of equations based on the information provided:

• Let x be the number of 6-blade packages sold.
• Let y be the number of 12-blade packages sold.
• Let z be the number of 24-blade packages sold.

Based on the package count and total blades sold:

1. 6x + 12y + 24z = 258 (total number of blades sold)
2. x + y + z = 12 (total number of packages sold)
3. 3x + 4y + 5z = 73 (total revenue)

We now have a system of three equations with three unknowns that we can solve using methods such as substitution, elimination, or matrices. After solving, we find that x = 6, y = 4, and z = 2, which corresponds to option b: 6 packages of 6 blades, 4 packages of 12 blades, 2 packages of 24 blades.