Question

100 Point test consist of two point questions and five point questions. There are a total of 44 questions on the test. How many questions of each type of test?

Answer 1

100 = 2x + 5y

44 = x + y

We can use elimination to solve this.

Multiply all terms in 2nd equation by 2.

88 = 2x + 2y

Subtract equation 2 from equation 1.

(100 = 2x + 5y) - (88 = 2x + 2y)

12 = 3y

Divide both sides by 3.

y = 4

The value of y is equal to 4, and so we can solve for the value of x.

44 = x + y

44 = x + 4

Subtract 4 from both sides.

40 = x

The value of x is equal to 40.

We can plug in the values to make sure our answer is correct.

100 = 2(40) + 5(4)

100 = 80 + 20

100 = 100 √ this is correct

44 = x + y

44 = 40 + 4

44 = 44 √ this is correct

And so, there are 40 two point questions, and 4 five point questions.

Explanation:

Answer 2

100 = 2x + 5y

44 = x + y

We can use elimination to solve this.

Multiply all terms in 2nd equation by 2.

88 = 2x + 2y

Subtract equation 2 from equation 1.

(100 = 2x + 5y) - (88 = 2x + 2y)

12 = 3y

Divide both sides by 3.

y = 4

The value of y is equal to 4, and so we can solve for the value of x.

44 = x + y

44 = x + 4

Subtract 4 from both sides.

40 = x

The value of x is equal to 40.

We can plug in the values to make sure our answer is correct.

100 = 2(40) + 5(4)

100 = 80 + 20

100 = 100 √ this is correct

44 = x + y

44 = 40 + 4

44 = 44 √ this is correct

And so, there are 40 two point questions, and 4 five point questions.