Question

It is the end of the semester, and the clubs at school are recording their profits. The Science Club started out with $20 and has increased its balance by an average of $10 per week. Write an equation in slope intercept form for the Science Club. It is the end of the semester, and the clubs at school are recording their profits. The Math Club has saved $5 per week after starting out with $50 at the beginning of the semester. Write an equation in slope intercept form for the Math Club. It is the end of the semester, and the clubs at school are recording their profits. Graph both lines from question 1 and 2 on the same coordinate plane. When do the clubs have the same balance?

Answer 1

Science Club- y=10x+20

Math Club- y=5x+50

They will be equal 6 weeks

Explanation:

X equals the number of weeks that have passed. In example of the science club, they would gain $10 every week, making the equation y (total money) equal to 10 dollars a week (or 10x.)

Since we know they begin with 20 dollars, we'll simply add that to the 10 dollars a week.

To find the week when they will be equal, we have to put both equations equal to each other.

10x+20=5x+50

Now we solve for x, or the number of weeks when the equations (and values) will be equal.

10x+20=5x+50

5x+20=50

5x=30

x=6

So... 6 weeks :)

You can use desmos to graph if you need it.