Carla and Benicio work in a men's clothing store. They earn commission from each suit and each pair of shows they sell. For selling 3 suits and one pair of shoes, Carla has earned $47 in commission. For selling 7 suits and 2 pairs of shoes, Benicio has earned $107 in commission. How much do the salespeople earn for the sale of a suit? For the sale of a pair of shoes?

Answer:

The salespeople earn for the sale of a suit = $13.

The salespeople earn for the sale of a pair of shoes = $8.

Step-by-step explanation:

Let x be the commission for each suit and y be commission for each pair of shoes.

We have been given that for selling 3 suits and one pair of shoes, Carla has earned $47 in commission. We can represent this information as:

We are also told that for selling 7 suits and 2 pairs of shoes, Benicio has earned $107 in commission. We can represent this information as:

We will use substitution method to solve our system of linear equations. From equation (1) we will get,

Substituting this value in equation (2) we will get,

Upon combining like terms we will get,

Therefore, the salespeople earn $13 for the sale of a suit.

Let us substitute x=13 in equation (1).

Therefore, the salespeople earn $8 for the sale of a pair of shoes.

Final answer:

The salespeople earn $13 for the sale of a suit and $8 for the sale of a pair of shoes.

Explanation:

To find out how much the salespeople earn for the sale of a suit and a pair of shoes, we can set up a system of equations using the given information. Let's denote the commission for a suit as 's' and the commission for a pair of shoes as 'p'. From the information given, we can write the following equations:

3s + p = 47

7s + 2p = 107

To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method:

From the first equation, we can solve for p in terms of s:

p = 47 - 3s

Substituting this expression for p into the second equation:

7s + 2(47 - 3s) = 107

Simplifying this equation:

7s + 94 - 6s = 107

s + 94 = 107

s = 13

Now that we know the commission for a suit is $13, we can substitute this value back into the first equation to find the commission for a pair of shoes:

3(13) + p = 47

39 + p = 47

p = 8

Therefore, the salespeople earn $13 for the sale of a suit and $8 for the sale of a pair of shoes.

Learn more about Commission rates here:

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