Question

Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 35 problems. Each problem is worth either 5 points or 2 points. How can you set up a system of equations to find how many problems of each point value are on the test? Let x = the number of questions worth 5 points. Let y = the number of questions worth 2 points.

A

Answer 1

x = 10 , y = 25

Explanation:

in the question we are provide with the required variables x , y

Number of problems with 5 points = x

Number of problems with 2 points = y

Total number of problems = 35

from the above details we can find first equation as,

x + y = 35 -----------------------(A)

total points from 5 point questions = 5x

total points from 2 point questions = 2x

Net total points = 100

now with this data we can find second equation as,

5x + 2y = 100 ------------------------(B)

solving (A) and (B) gives us value of x and y

multiply (A) with 2 and subtracting it from (B) gives us

3x = 30

x = 10

y = 35 - x = 35 -10 = 25

Answer 2

x + y = 35

5x + 2y = 100

Explanation:

If x is the number of questions worth 5 points and y is the number of questions worth 2 points.

Now, it is said that there is a total of 35 questions.

So, x + y = 35 ....... (1)

Again, the test worth 100 points.

Hence, 5x + 2y = 100 .......... (2)

Therefore, the equations (1) and (2) are the system of equations to find x and y. (Answer)