Question

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

Answer 1

To solve the problem, we formulate two equations based on the total number of problems and their point values. After solving the system of equations, we find that there are 8 problems worth 5 points each and 30 problems worth 2 points each.

Step-by-step explanation:

To solve the problem of determining how many problems of each point value are on a 100-point math test with 38 problems, each worth either 5 points or 2 points, we can set up a system of equations.

Step-by-Step Explanation

1. Let the number of 5-point problems be x and the number of 2-point problems be y.
2. The total number of problems is 38, which gives us the equation x + y = 38.
3. The total value of the problems is 100 points, leading to the second equation 5x + 2y = 100.
4. Now we solve this system of equations. Multiplying the first equation by 2 (to align the coefficients of y) gives us 2x + 2y = 76.
5. Subtracting this new equation from the second equation (5x + 2y = 100 - 2x - 2y = 76) gives us 3x = 24.
6. Dividing both sides of the equation by 3 yields x = 8. This tells us there are 8 problems worth 5 points each.
7. Substituting x back into the first equation (x + y = 38) gives us 8 + y = 38. Solving for y yields y = 30.

Therefore, there are 8 problems worth 5 points each and 30 problems worth 2 points each on the math test.

Answer 2

5 points question is 8

and 2 points questions is 30 !!

Step-by-step explanation:

Let the number of 5 points questions be x and number of the 2 points questions be y !!

Given :- The paper has 38 problems

i.e,

number of 5 points Q + number of 2point Q = 38

=> x + y = 38

=> x = 38 - y .... ( i )

And , The test worth 100 pts :-

There must be x number of Questions which carry 5 points and there must y number of questions which carries 2 points ( as assume above )

so, 5x + 2y = 100 .... ( ii )

Putting value of the x in ( ii )

5 ( 38 - y ) + 2y = 100

190 - 5y + 2y = 100

- 3y = - 90

y = 30

Putting value of y in ( i )

x = 38 - y

x = 38 - 30

x = 8

So, the Number of 5points Question is

x = 8

and , the number of 2 points questions is y = 30 !!