Your teacher is giving you a test worth 100 points containing 40 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test?

Sep 11, 2015

Number of 2 mark questions $= 30$
Number of 4 mark questions $= 10$

Explanation:

Let x be the number of 2 mark questions
Let y be the number of 4 mark questions

$x + y = 40$ ---------------(1)
$2 x + 4 y = 100$---------------(2)

Solve equation (1) for y
$y = 40 - x$

Substitute $y = 40 - x$ in equation (2)

$2 x + 4 \left(40 - x\right) = 100$
$2 x + 160 - 4 x = 100$
$2 x - 4 x = 100 - 160$
$- 2 x = - 60$
$x = \frac{- 60}{- 2} = 30$

Substitute $x = 30$ in equation (1)

$30 + y = 40$
$y = 40 - 30 = 10$
Number of 2 mark questions $= 30$
Number of 4 mark questions $= 10$