Mathematics, 26.06.2019 19:00 CHRONICxDJ

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?

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Answer from: arlabbe0606

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:

3x+y=47...(1)

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:

7x+2y=107...(2)

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

y=47-3x

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

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

7x+94-6x=107

Upon combining like terms we will get,

7x-6x=107-94

x=13

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

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

3*13+y=47

39+y=47

y=47-39

y=8

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

Answer from: Quest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

Answer from: Quest

And is b i hoped this

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Carla and benicio work in a men's clothing store. they earn commission from each suit and each pair...