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 four shirts cost ​$47​, while four sweaters and three shirts cost ​$84​, find the price of one sweater and the price of one shirt.

Answer 1

Explanation:

Let x be the sweater

Let y be the shirt

Equation1: x+4y=47

Equation2: 4x+3y=84

Now solve for x in the first equation:

x+4y=47

x=47-4y

Now that we've solved for x, substitute the value for x which is 47-4y into Equation2 as follows:

4x+3y=84

4(47-4y)+3y= 84

188-16y+3y= 84

188-13y= 84

-13y= 84-188

-13y= -104

y= -104/-13

y= 8

Now plug in the value for y which is 8 into Equation 1 and solve for x:

x+4y=47

x+4(8)=47

x+32=47

x=47-32

x=15

You can perform a check by plugging in the x and y values into equations 1 and 2 which should yield true statements.

The answer is: 1 sweater costs $15 and 1 shirt costs $8