find the price of one sweater and the price of one shirt

Question

in a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. if one sweater and three shirts cost $39, while three sweaters and two shirts cost $54, find the price of one sweater and the price of one shirt.

Answer 1

Let x be the cost of one sweater.

Let y be the cost of one shirt.

 

From the information given:

 

X + 3Y = 39 and 3X + 2Y = 54

 

I suggest we solve the first equation for Y and then substitute that result into the second equation and solve for X.

 

X + 3Y = 39

      3Y = 39 - X

        Y = 39 - X  

               3    3

        Y = 13 - (1/3)X  (Now let's substitute this value for Y into the second equation and solve for X.)

 

3X + 2Y = 54

3X + 2(13 - (1/3)X) = 54

3X + 26 - (2/3)X = 54

3X   -  (2/3)X  =  54 - 26

 

(9/3)X - (2/3)X = 28

 

(7/3)X = 28

 

X= 28(3/7) = 4(3)= 12  (So, the price of one sweater is $12).

Since the price of one shirt is Y = 13 - (1/3)X then:

 

Y = 13 - (1/3)12 = 13 - 4 = 9

 

The price of one shirt is $9.

Answer 2

A = price of one sweater

B = price of one shirt

Given A+3B =39

and 3A +2 B = 54

Using substitution

A = 39 -3B

3(39 -3B) + 2B =54

117 -9B +2B = 54

or 

-7B =-117 +54

7B = 63

 B= 9

but A= 39-3B = 39 -27= 12 

Shirt = $9 each

Sweater = $12 each