Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. A boutique in Greenwood specializes in leather goods for men. Last month, the company sold 67 wallets and 78 belts, for a total of $5,669. This month, they sold 60 wallets and 14 belts, for a total of $3,848. How much does the boutique charge for each item?

Answer 1

To find the prices of wallets and belts sold by a boutique, we create a system of equations based on monthly sales data, solve it using the elimination method, and find that the boutique charges $57.43 for a wallet and $23.48 for a belt.

Step-by-step explanation:

The scenario is regarding a boutique that sells leather goods and we have the data for two different months for the number of wallets and belts sold as well as the total revenue for each month. To determine the price of each item, we need to establish a system of linear equations that we can solve using the elimination method.

Step 1: Define the variables

Let's define Pw as the price of one wallet and Pb as the price of one belt.

Step 2: Formulate the system of equations

Using the first month's data, we can write the first equation as:

67Pw + 78Pb = $5,669 (Equation 1)

Using the second month's data, we arrive at the second equation:

60Pw + 14Pb = $3,848 (Equation 2)

Step 3: Solve the system using elimination

To apply the elimination method, we will multiply the second equation by 4.5 to align the Pb terms:

270Pw + 63Pb = $17,316 (Equation 3 - after multiplying Equation 2 by 4.5)

Now we subtract Equation 1 from Equation 3:

203Pw = $11,647 => Pw = $11,647 / 203 => Pw = $57.43

Now that we have Pw, we can plug it into Equation 1 to solve for Pb:

67($57.43) + 78Pb = $5,669 => 3847.81 + 78Pb = $5,669 => 78Pb = $5,669 - 3847.81 => Pb =$23.48

Therefore, the boutique charges $57.43 for a wallet and $23.48 for a belt.