Question 620820: 9. Your teacher is giving you a test worth 100 points containing 25 questions. You are told there are 3-point and 8-point questions on the test. How many of each type are on the test?
Found 2 solutions by ewatrrr, math-vortex:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
test worth 100 points containing 25 questions with 3-pt and 8-pt questions
How many of each type are on the test?
3x + 8(25-x) = 100
-5x = -100
x = 20, 3-pt and 5 8pt qestions.
CHECKING our Answer***
60 + 40 = 100
Answer by math-vortex(648)  (Show Source):
You can put this solution on YOUR website! Hi, there--
.
We can solve this problem by creating a system of two linear equations.
.
STEP I: Define your variables
Let x be the number of 3-point questions.
Let y be the number of 8-point questions.
.
STEP II: Using information given in the problem, create equations that model the situation.
We know that the test has 25 questions, so
.
[the number of 3-point questions] + [the number of 8-point questions] = [25 questions]
.
In algebra, we write,
x+y=25
.
We know that the test has a total of 100 points, so
.
[points you can get from 3-pt. questions} + [points you can get from 8-pt. questions] = [100 pts.]
.
The total points you could get from 3-pt. questions is 3 times the number 3-pt. questions you have. That's our variable x. So, in algebra, we write, 3x. By similar reasoning, the total points you could get from 8-pt. question is 8y. Our equation is
.
3x+8y=100
.
STEP III: Solve the system of equations using the elimination method.
Multiply every term in the first equation by -3.
.
x + y = 25 ---> -3x -3y = -75.
.
Add the first and second equations together. Notice that -3x and 3x cancel each other out since their sum is zero; -3y+8y=5y and -75+100=25. This leaves us with one equation,
.
-3x -3y = -75
3x + 8y = 100
--------------
5y = 25
.
Solve for y by dividing both sides of the the resulting equation by 5.
.
y = 5
.
In the context of your problem, y = 5 means that there are five 8-pt. questions. Since there are 25 questions all together, there must be twenty 3-pt. questions (5+20=25).
.
STEP IV: Check your work.
We need to make sure the points work out for the x and t values we found. Five 8-pt. questions are worth 40 points (5*8=40). Twenty 3-pt. questions are worth 60 points (20*3=60). Thus the test is worth 100 point altogether (40+60=100).
.
Hope this helps! Feel free to email if you still have questions about this.
.
Ms.Figgy
math.in.the.vortex@gmail.com
Your teacher is giving you a test worth 100 points containing 25 questions. You are told there are 3-point and 8-point questions on the test. How many of each type are on the test?
|
|
|
