Question

Your next Algebra test has a mix of 20 problems. Some problems are worth 4 points, and others are worth 6 points. The test is worth 100 points total. How many of each type of problem are on the test?

A. 10 problems worth 4 points and 10 problems worth 6 points
B. 12 problems worth 4 points and 8 problems worth 6 points
C. 14 problems worth 4 points and 6 problems worth 6 points
D. 16 problems worth 4 points and 4 problems worth 6 points

Answer 1

The test contains 10 problems worth 4 points and 10 problems worth 6 points. This was determined by setting up two equations based on the total problems and the total points, and solving for the number of problems of each point value.

Step-by-step explanation:

To determine how many problems of each point value are on an Algebra test with a total of 20 problems worth 100 points, we can set up a system of equations. Let's denote x as the number of problems worth 4 points and y as the number of problems worth 6 points. We are given two conditions:

• The total number of problems is 20: x + y = 20.
• The total value of the problems is 100 points: 4x + 6y = 100.

Now we solve this system of equations. First, we can multiply the first equation by 4 to help us eliminate one variable:

1. 4x + 4y = 80 (first equation multiplied by 4).
2. 4x + 6y = 100 (second equation).

Subtracting the first modified equation from the second gives us:

• 2y = 20.

Dividing both sides of this equation by 2, we get y = 10. Now that we have the value for y, we can substitute it back into the first equation to find x:

• x + 10 = 20
• x = 10

So, there are 10 problems worth 4 points and 10 problems worth 6 points (Option A).