Answer
4 years
Work Step by Step
First lets analyze the problem and set variables for each piece of information. For both problems, we will set x as the number of years passed and y as the number of songs written.
For Jay, our equation has a y-intercept of 24 because he has already written 24 songs to this date. Next, our slope for Jay is 6 because that is the rate at which he writes songs annually. So we can write Jay's equation as
1. y=6x+24
Now lets write the equation for Jenna. To this date, Jenna has not written any songs so her equation's y-intercept is 0. Next, her slope is 12 because that is the rate at which she writes her songs annually. So in total, her equation can be written as:
2. y=12x
Now we have to find the years after which both have the same number of written songs. We do this by finding the intersection of the two lines. When we graph both equations using intercepts and slopes, we get that the point at which the two lines intersect is (4, 48)
We only take in account the x-coordinate because that is the number of years it takes for both to write the same number of songs. So, 4 years from now, Jenna will have written the same number of songs as Jay.
