Question

A boutique in Riverside specializes in leather goods for men. Last month, the company sold 25 wallets and 62 belts, for a total of $3,150. This month, they sold 78 wallets and 19 belts, for a total of $5,467. How much does the boutique charge for each item? The boutique charges $___ for a wallet, and $___ for a belt.

Answer 1

By setting up a system of equations from the sales information and solving it using the elimination method, we find that the boutique charges $63.65 for a wallet and $25.14 for a belt.

Step-by-step explanation:

To determine how much the boutique charges for each item (wallet and belt), we need to set up a system of equations based on the information provided. Let w be the price of a wallet and b be the price of a belt. The two equations are derived from the sales information:

25w + 62b = $3,150 (Last month's sales)

78w + 19b = $5,467 (This month's sales)

Now, we need to solve this system of linear equations. We can use either substitution or elimination method. Here, I will use the elimination method:

Multiply the first equation by 78 and the second by 25 to make the coefficients of w equal:

1950w + 4836b = $246,300

1950w + 475b = $136,675

Subtract the second equation from the first to eliminate w:

4361b = $109,625

Now, divide both sides by 4361 to find the price of a belt:

b = $25.14

Substitute the value of b into the first original equation to find the price of a wallet:

25w + 62($25.14) = $3,150

25w + $1,558.68 = $3,150

25w = $3,150 - $1,558.68

25w = $1,591.32

w = $63.65

The boutique charges $63.65 for a wallet, and $25.14 for a belt.

Answer 2

The boutique charges $64 for a wallet, and $25 for a belt.

Step-by-step explanation:

We can write two equations using the information we are given. The we solve the system of equations to find the prices.

Let w = price of 1 wallet.

Let b = price of 1 belt.

"Last month, the company sold 25 wallets and 62 belts, for a total of $3,150."

25w + 62b = 3150

"This month, they sold 78 wallets and 19 belts, for a total of $5,467."

78w + 19b = 5467

We now have the following system of 2 equations in 2 unknowns.

25w + 62b = 3150

78w + 19b = 5467

We will use the substitution method.

Solve the first equation for w.

25w + 62b = 3150

25w = -62b + 3150

w = -62/25 b + 126

Now substitute w with -62/25 b + 126 in the second equation, and solve for b.

78w + 19b = 5467

78(-62/25 b + 126) + 19b = 5467

-4836/25 b + 9828 + 19b = 5467

-4836/25 b + 19b = -4361

Multiply both sides by 25.

-4836b + 475b = -109,025

4361b = 109,025

b = 25

Now we substitute 25 for b in the first original equation and solve for w.

25w + 62b = 3150

25w + 62(25) = 3150

25w + 1550 = 3150

25w = 1600

w = 64

Answer: The boutique charges $64 for a wallet, and $25 for a belt.