Three friends went shopping at their favorite store. All the pants, shirts, and sweaters were on sale, and articles of each type cost the same.

Question

Clothing purchases and cost 

cost   #of pants #of shirts #of swe.

Alicia.      5          5          2     $377

Bette       5          6          0     $322

Cara        3          7          3     $408

Answer 1

I assume you need to find the cost of a pair of pants, a sweater, and a shirt...

 

Let P = cost of pants

Let B = cost of a shirt (blouse)

Let S = cost of a sweater

 

We have 3 equations and 3 variables from the table as given:

 

eqn 1)  5P + 5B + 2S = 377

eqn 2)  5P + 6B         = 322

eqn 3)  3P + 7B + 3S = 408

 

Let's take eqn1 and eqn 2 and eliminate the P variable

Multiply eqn 2 by -1 and add the result to eqn 1

 

 5P + 5B + 2S = 377   eqn 1

-5P - 6B          = -322  eqn 2(-1)

------------------------

        -B + 2S = 55

 

Now let's use eqn 2 and eqn 3 to eliminate the P variable again

 

-15P - 18B            = -966    eqn 2(-3)

 15P + 35B + 15S = 2040    eqn 3(5)

----------------------------

          17B + 15S = 1074

 

 

I now have two equations with two variable that I can use to solve for B and S

 

   -B + 2S = 55

17B + 15S = 1074

 

We will follow the same process to eliminate one variable and solve for the other

I will multiply the 1st by 17 to eliminate the B variable when I add the results

 

-17B + 34S = 935

 17B + 15S = 1074

----------------------

           49S = 2009

               S = 2009/49

               S = 41

 

We now have the cost of a sweater...  Substitute 41 in place of S

in the equation -B + 2S = 55  or  17B + 15S = 1074 to solve for B

I will use -B + 2S = 55

 

-B + 2(41) = 55

-B + 82 = 55

-B = 55-82

-B = -27

 B = 27

 

We now have the cost of a sweater S=41 and the cost of a shirt B=27

Substitute those values back into one of the original 3 equations to find

the cost of a pair of pants:

 

I'll use equation 2:  5P + 6B = 322

                             5P + 6(27) = 322

                            5P + 162 = 322

                            5P = 322-162

                            5P = 160

                              P = 32

 

A pair of pants costs $32

A shirt costs $27

A sweater costs $41