Your math teacher tells you that next week's test is worth 100 points and contains 38 problems. Each problem is worth either 5 points or 2 points. Because you are studying systems of linear equations, your teacher says that for extra credit you can figure out how many problems of each value are on the test. How many of each value are there?
let the number of 5 pointers be x
let the number of 3 point questions be y
x + y = 38
5x + 3y = 100
Since "you are studying systems of linear equations, your teacher says that for extra credit you can figure out how" to solve this.
OOPS, misread your questions, should have put on my reading glasses.
change "3 point question" to "2 point question" and the last equation to
5x + 2y = 100
To figure out how many problems of each value are on the test, we can set up a system of linear equations.
Let's denote:
x = the number of problems worth 5 points
y = the number of problems worth 2 points
From the problem statement, we have two pieces of information:
1) The total number of problems is 38:
x + y = 38
2) The total value of the test is 100 points:
5x + 2y = 100
Now we have a system of two equations with two variables. We can solve this system using various methods such as substitution, elimination, or matrix row operations.
Let's solve it using the substitution method.
From equation (1), we can solve for x:
x = 38 - y
Substitute this expression for x in equation (2):
5(38 - y) + 2y = 100
Now, simplify and solve for y:
190 - 5y + 2y = 100
-3y = -90
y = 30
Substitute this value of y back into equation (1):
x + 30 = 38
x = 8
Therefore, there are 8 problems worth 5 points and 30 problems worth 2 points on the test.