The ratio of essay questions to total number of question be 10: 14
Let the number of total questions = x
The teacher wants the essay questions to be fewer than 10 on the quiz
The essay questions = x - 10
To solve for x, we need to establish a proportion
10 / x - 10 = 14/x
Cross multiply
14(x - 10) = 10 * x
14x - 140 = 10x
Collect the like terms
-140 = 10x - 14x
-140 = -4x
Divide both sides by -4
-140/-4 = -4x/-4
x = 140/4
x = 35
The total questions on the quiz is 35
Since, essay questions is