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

Nov 14, 2016

If all the questions were 2-pt questions there would be 80 points total, which is 20 pt short.

#### Explanation:

Every 2-pt replaced by a 4-pt will add 2 to the total.
You'll have to do this $20 \div 2 = 10$ times.

Answer: $10$ 4-pt questions and $40 - 10 = 30$ 2-pt questions.

The algebraic approach:
We call the number of 4-pt qustions $= x$
Then the number of 2-pt questions $= 40 - x$

Total points: $= 4 \cdot x + 2 \cdot \left(40 - x\right) = 100$
Working away the brackets:
$4 x + 80 - 2 x = 100$

Subtract 80 on both sides:
$4 x + \cancel{80} - \cancel{80} - 2 x = 100 - 80$

$\to 2 x = 20 \to x = 10$ 4-pt questions
$\to 40 - x = 40 - 10 = 30$ 2-pt questions.