Question

Mr. Martin’s math test, which is worth 100 points, has 35 problems. Each problem is worth either 5 points or 2 points. Let x = the number of questions worth 5 points. Let y = the number of questions worth 2 points. x + y = 35, 5x + 2y = 100 How many problems of each point value are on the test? 10 problems worth 5 points and 25 problems worth 2 points 15 problems worth 5 points and 20 problems worth 2 points 20 problems worth 5 points and 15 problems worth 2 points 25 problems worth 5 points and 10 problems worth 2 points

Answer 1

The answer is 10 problems worth 5 points and 25 problems worth 2

Explanation:

we take our equation

5x+2y=100

then we put in our x & y

5(10)+2(25)

50+50

100

The first answer is the only one that gets you to 100

Answer 2

10 problems worth 5 points and 25 problems worth 2 points

Explanation:

Let x = the number of questions worth 5 points.

Let y = the number of questions worth 2 points

x+y = 35 since there are 35 problems

5x + 2y = 100 since there are 100 points

Multiply the first equation by -5 so we can eliminate x

-5(x+y) = 35*-5

-5x -5y =-175

Add this to the second equation

-5x -5y =-175

5x + 2y = 100

-----------------------

-3y = -75

Divide each side by -3

-3y/-3 = -75/-3

y = 25

There are 25 2 point questions

Now find x

x+y = 35

x+25 = 35

x = 35-25

x =10

There are 10 5 point questions