A math test is worth 100 points and has 38 problems. Each problem is worth either 5 or 2 points. How many problems of each point value are on the test?
let F be the number of five point questions, and T be the other.
5F+2T=100
F+T=38
can you take it from there?
T=2
F=3
Let's assume that there are x problems worth 5 points and y problems worth 2 points on the test.
The problem statement tells us that there are 38 problems in total, so we have the equation:
x + y = 38 ...(Equation 1)
It is also given that the test is worth 100 points. Since each problem is worth either 5 or 2 points, we can write another equation:
5x + 2y = 100 ...(Equation 2)
Now we have a system of two equations with two variables. We can solve this system by substitution or elimination method.
Let's solve it using the elimination method:
Multiply Equation 1 by 2:
2x + 2y = 76
Subtract Equation 2 from the equation above:
(2x + 2y) - (5x + 2y) = 76 - 100
2x + 2y - 5x - 2y = -24
-3x = -24
Divide both sides of the equation by -3:
(-3x)/(-3) = (-24)/(-3)
x = 8
Substitute the value of x into Equation 1:
8 + y = 38
y = 38 - 8
y = 30
Therefore, there are 8 problems worth 5 points and 30 problems worth 2 points on the test.
To find the number of problems of each point value on the test, we can set up a system of equations based on the given information.
Let's say the number of problems worth 5 points is 'x', and the number of problems worth 2 points is 'y'.
From the problem statement, we have two pieces of information:
1) The total number of problems on the test is 38:
x + y = 38
2) The total point value of the test is 100:
5x + 2y = 100
To solve this system of equations, we can use a method called substitution or elimination.
Let's solve this system using the substitution method:
1) Solve the first equation for 'x':
x = 38 - y
2) Substitute this value of 'x' in the second equation:
5(38 - y) + 2y = 100
3) Simplify and solve for 'y':
190 - 5y + 2y = 100
-3y = 100 - 190
-3y = -90
y = -90 / -3
y = 30
4) Substitute the value of 'y' back into the first equation to find 'x':
x + 30 = 38
x = 38 - 30
x = 8
Therefore, there are 8 problems worth 5 points and 30 problems worth 2 points on the test.