Question

A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 points. How many 4-point problems are there in the test ?

Answer 1

To find the number of 4-point problems on a math test, we set up a system of linear equations based on the total number of problems and the total points. By solving these equations, we can determine there are 10 4-point problems on the test.

Step-by-step explanation:

The question requires us to solve for the number of 4-point problems on a math test that consists of problems worth either 3 points or 4 points and adds up to a total of 100 points. Let's denote the number of 3-point problems as x and the number of 4-point problems as y. The total number of problems is given as 30, which leads to our first equation:

x + y = 30

Each 3-point problem adds 3 points to the total score, and each 4-point problem adds 4 points, summing up to 100 points. Therefore, we create our second equation based on the points:

3x + 4y = 100

We now have a system of linear equations to solve:

1. x + y = 30
2. 3x + 4y = 100

By solving these equations simultaneously, typically by substitution or elimination, we can determine the value of y, which represents the number of 4-point problems on the test.

Let's use the substitution method:

1. Solve the first equation for x: x = 30 - y
2. Substitute x into the second equation: 3(30 - y) + 4y = 100
3. Simplify and solve for y:

90 - 3y + 4y = 100

y = 100 - 90

y = 10

Thus, there are 10 4-point problems on the test, with the remaining 20 problems being worth 3 points each.

Answer 2

I think there's 24 4-point probs