Question

A boutique in Oak Grove specializes in leather goods for men. Last month, the company sold 15 wallets and 48 belts, for a total of $2,358. This month, they sold 38 wallets and 20 belts, for a total of $1,808. How much does the boutique charge for each item?

Answer 1

The system of linear equations based on the boutique's sales is solved using the elimination method, yielding the price of $26 for wallets and $41 for belts.

Step-by-step explanation:

Solving a System of Equations

The boutique in Oak Grove's sales can be represented by a system of linear equations. Let's denote wallets as w and belts as b. The equations based on last month's sales would be:

1. 15w + 48b = 2358
2. 38w + 20b = 1808

To solve for w and b, we can use either substitution or elimination. We'll use the elimination method here by multiplying the second equation by 2.4 to make the b coefficients equal and then subtract the first equation from it:

1. (2.4)(38w + 20b) = (2.4)(1808)
2. 91.2w + 48b = 4339.2
3. 91.2w + 48b - (15w + 48b) = 4339.2 - 2358
4. 76.2w = 1981.2
5. w = 1981.2 / 76.2
6. w = 26

Now that we have w = 26, we can substitute w into any of the original equations to solve for b:

1. 15(26) + 48b = 2358
2. 390 + 48b = 2358
3. 48b = 2358 - 390
4. 48b = 1968
5. b = 1968 / 48
6. b = 41

Therefore, the boutique charges $26 for each wallet and $41 for each belt.