if one sweater and four shirts cost $53, while five sweaters and two shirts cost $103.

Question

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

Answer 1

With this information, you can set up two equations as follows:

 

1(sweater) + 4(shirts) = 53

5(sweaters) + 2(shirts) = 103

 

We can then solve this equation using a principle called substitution.  It puts one variable in terms of the other, like so:

 

1(sweater) = 53 - 4(shirts)

 

Now that we know what one sweater equals (based on the first equation), we can substitute this value into the second equation:

 

5(53 - 4(shirts)) + 2(shirts) = 103

 

And now we solve for "shirts"

 

265 - 20(shirts) + 2(shirts) = 103

-18(shirts) = -162

shirts = $9

 

To get the price of a sweater, plug in the value of the shirt to the first or second equation.  I will use the first equation:

 

1(sweater) + 4(shirts) = 53

1(sweater) + 4(9) = 53

sweater = $17