We want to find out how many sweatshirts and hats we buy to stock our school store. Let's begin by using a verbal model to write a system of linear equations. We will use x to represent the number of sweatshirts and y to represent the number of hats.
From the exercise, we know that we buy a combined total of 25 sweatshirts and hats for $ 172.50. Each sweatshirt costs $ 8.00 and each hat costs $ 2.50. Now we are ready to write the system of equations!
x+ y= 25 & (I) 8* x+ 2.5* y= 172.5 & (II)
Next, we will use the Substitution Method to solve the system we created. First, let's isolate x on one side of Equation (I).
x+y=25 ⇕ x=25-y
Now we are ready to solve the system. We will substitute 25-y for x in Equation (II) and solve the equation for y.
