Let p, r, and h be the number of pop, rock, and hip-hop songs, respectively. Form and solve a system of equations.
144 pop songs, 48 rock songs and 80 hip-hop songs
Practice makes perfect
Let's solve this exercise by writing and solving a system of equations. To do so, we first need to define the variables. Let p, r, and h be the number of pop, rock, and hip-hop songs, respectively, that are played during a day by the radio station.
Writing the System
We are told that a total of 272 songs are played. Therefore, the sum of the three variables must equal 272.
p + r + h=272
We are also told that the number of pop songs is 3 times the number of rock songs. Moreover, the number of hip-hop songs is 32 more than the number of rock songs. We can write two more equations using this information.
p = 3 r and h = r + 32
The three equations we have written form a system of equations.
p+r+h=272 & (I) p=3r & (II) h=r+32 & (III)
Solving the System
If we pay close attention to the system, we can see that in Equation (II) and Equation (III) the p- and h-variables are isolated. This means that the most convenient method to solve our system is the Substitution Method. Let's substitute 3r and r+32 for p and h, respectively, in Equation (I).
