Write the expressions for the total amount the student council spent each year, and set them equal to the given values.
8 registrations and 6 T-shirts, see solution.
Practice makes perfect
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.
15x+10y
We are also told that this sum is $180. Let's set 180 equal to the above expression and form an equation.
15x+10y=180
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.
12x+9y=150
Using the first and second equation, we can write the following system of equations.
15x+10y=180 & (I) 12x+9y=150 & (II)
Let's solve it by substitution. We will solve Equation (I) for y and substitute its equivalent value into Equation (II).
