Exercise 14 Page 208

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.

8x+2.5y=172.5

Substitute

x= 25-y

8( 25-y)+2.5y=172.5

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Solve for y

Distr

Distribute 8

200-8y+2.5y=172.5

AddTerms

Add terms

200-5.5y=172.5

SubEqn

LHS-200=RHS-200

-5.5y=-27.5

DivEqn

.LHS /(-5.5).=.RHS /(-5.5).

y=5

We can substitute 5 for y in either equation to solve for the value of x. Let's substitute it into Equation (I) for simplicity.

x+y=25

Substitute

y= 5

x+ 5=25

SubEqn

LHS-5=RHS-5

x=20

We found that we bought 20 sweatshirts and 5 hats for our school shop.