Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

A boutique in Newport specializes in leather goods for men. Last month, the company sold 39 wallets and 38 belts, for a total of $2,566. This month, they sold 48 wallets and 69 belts, for a total of $4,203. How much does the boutique charge for each item? The boutique charges $ for a wallet and $ for a belt. The boutique charges how much money for a wallet, and how much money for a belt?

Answer 1

39w + 38b = 2566

48w + 69b = 4203

Now can you solve or do you have a question?

Answer 2

First define your variables. In looking at the questions ("The boutique charges how much money for a wallet, and how much money for a belt?") we can see that what we do not know is the cost of the wallet and the belt. So, we make a variable for each. Let "w" be the cost of a wallet and let "b" be the cost of a belt.

We are told that 39 wallets and 38 belts were sold for $2,566. So multiplying the cost of each wallet (which we defined as "w") by 39 will give us the amount we earned from wallets. That would be "39w". And multiplying the cost of each belt by 38 will give us the amount we earned from belts. That would be "38b". And adding them together results in a total of $2566 so:

39w + 38b = 2566

We are also told that they sold 48 wallets and 69 belts for a total of $4,203 so:

48w + 69b = 4203

We can make this equation a little simpler by dividing both sides by 3:

16w + 23b = 1401

So, we need to solve these two equations:

1) 39w + 38b = 2566

2) 16w + 23b = 1401

It's not easy, by, I'll choose to use Elimination. I will multiply Equation 1) by -16 and I will multiply Equation 2) by 39 then add the equations together:

1A) -624w - 608b = -41056

2A) 624w + 897b = 54639

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289b = 13583

b = 13583/289 = 47

We can now use one of the equations, I'll choose 2), to plug in b = 47 and solve for w:

16w + 23(47) = 1401

16w + 1081 = 1401

16w = 320

w = 20

So wallets were priced at $20 and belts were priced at $47