The seniors at Travis High School have three purchase options for their yearbook.
Option 1: They can purchase a copy of the yearbook and a one-page ad for $35.
Option 2: They can purchase a copy of the yearbook and a one-half page ad for $25.
Option 3: They can purchase a copy of the yearbook for $15.
Last year, the yearbook committee sold 475 yearbooks for a total of $13,275. Forty-five more seniors chose option 1 than option 2. How many seniors chose each of the three different options?
x chose option 2
x+45 chose option 1
the rest (475-x-(x+45)) chose neither
now add up all the money
35(x+45)+25x+15(430-2x) = 13275
solve for x and then you're on your way.
To solve this problem, we need to set up a system of equations based on the given information.
Let's denote the number of seniors who chose Option 1 as "x", the number of seniors who chose Option 2 as "y", and the number of seniors who chose Option 3 as "z".
Based on the given information, we can set up the following equations:
Equation 1: x + y + z = total number of seniors
Equation 2: 35x + 25y + 15z = total revenue from yearbook sales
Equation 3: x = y + 45 (since 45 more seniors chose Option 1 than Option 2)
Now, let's substitute Equation 3 into Equation 1 to eliminate one variable:
(y + 45) + y + z = total number of seniors
2y + z + 45 = total number of seniors (Equation 4)
Next, let's subtitute Equation 3 into Equation 2:
35(y + 45) + 25y + 15z = 13,275
35y + 1575 + 25y + 15z = 13,275
60y + 15z = 11,700 (Equation 5)
Now we have a system of two equations with two variables: Equation 4 and Equation 5.
Solving this system of equations will give us the values of "y" and "z". Then, we can substitute those values into Equation 3 to find the value of "x".
Let me do the calculations for you.