Presentation Transcript
Writing Equations to Solve Word Problems :Writing Equations to Solve Word Problems Ms. Zappella is going to take the entire 8th grade to the movies. The movie theater offers a deal: for $100 they will give her unlimited pop corm for all of the students no matter how many she takes, and they will only charge her $5 per student for their movie ticket. How much will it cost in total if she takes 130 students?
Ask yourself….. :Ask yourself….. What is the given information?
What is the question asking?
Define your variables (usually 2) $100 dollars for popcorn
$5 per student
130 students
How much is the total cost if there are 130 students?
C = total cost
S= number of students
A word about variables… :A word about variables… Remember Slope-Intercept Form?
Y = mx +b
Y is what the whole thing is equal to.
M is the slope (SLOPE IS CONSTANT!)
X is the variable that causes the change.
B is the y-intercept (it only happens once!)
Filling in y = mx+b…Y :Filling in y = mx+b…Y Since y is what the whole thing is supposed to equal (the total), what do we want our whole equation to be equal to in the end (what total are we looking for?)
The total Cost,
or C
So now we have, C=….
m :m Now we need m. We know slope is a constant, or something that happens over and over again? In other words, which number in the given information is going to be used more than once?
5, because every student (all 130 of them) has to pay $5
So the slope of this equation is 5
So now we have C= 5….
x :x X is the number that causes the change. In this problem, what is going to cause the total to change?
S, the number of students
(the more students, the more it will cost)
So now we have C= 5s…..
+b :+b B is the y-intercept. It’s the number that only gets used once, doesn’t change, and gets used no matter what.
In this problem, what number will get used only once? In other words, what will Ms. Z have to pay if she brings 1 student or 130?
100. Ms. Z has to pay $100 dollars for pop corn no matter what.
That’s it!
Our equation is C = 5s +100 which means
The total cost is equal to $5 times the number of students plus $100.