Exercise 13 Page 591

Let $x$ be the number of registrations and $y$ be the number of T-shirts bought each year by the student council. This year the registration for a conference costs $\$15,$ and the T-shirt costs $\$10.$ By multiplying $15$ by $x$ and $10$ by $y$ and adding these expressions, we can find how much the student council will spend for the conference. We are also told that this sum is $\$180.$ Let's set $180$ equal to the above expression and form an equation. Last year, they spent $\$12$ per registration and $\$9$ per T-shirt for a total of $\$150$ to buy the same number of registrations and T-shirts. Similarly, multiplying $12$ by $x$ and $9$ by $y$ and adding these expressions, we can find how much they spent in total. Then, we can set it equal to $\$150$ to form an equation. Using the first and second equation, we can write the following system of equations. Let's solve it by substitution. We will solve Equation (I) for $y$ and substitute its equivalent value into Equation (II). The student council bought $8$ registrations for the conference and $6$ T-shirts each year.