#### evan_thomas

##### New member
30 questions on a test that are either history or geography. They answer 24 more questions CORRECTLY than they do INCORRECTLY. They answer 14 of the 16 history questions correctly. How many geography questions do they answer correctly? If you can break this down and explain simply that would be very nice. Thank you

30 questions on a test that are either history or geography. They answer 24 more questions CORRECTLY than they do INCORRECTLY. They answer 14 of the 16 history questions correctly. How many geography questions do they answer correctly? If you can break this down and explain simply that would be very nice. Thank you

Since you posted this under arithmetics, I find making a 2-way table helps. Can you try to fill out the blank cells?

 History Geography Total Correct 14 Incorrect Total 16 30

30 questions on a test that are either history or geography. They answer 24 more questions CORRECTLY than they do INCORRECTLY. They answer 14 of the 16 history questions correctly. How many geography questions do they answer correctly? If you can break this down and explain simply that would be very nice. Thank you
I absolutely loathe this sort of question. It is a basic question in algebra, but they give it to students who do not know algebra.

Quick introduction to algebra. To help us think about unknown numbers, we give them temporary names using the letters of the alphabet.

w = the number of wrong answers
c = the number of correct answers.

What do we know about these numbers? Well, [imath]c - w = 24[/imath]. How do we know that? Also we know that [imath]c + w = 30.[/imath] How do we know that?

When you learn algebra, you will learn mechanical ways to figure out what numbers are represented by c and w. But you don’t need those techniques to solve this easy a problem. Think about what pair of numbers c and w make c - w = 24 and c + w = 30?

30 questions on a test that are either history or geography. They answer 24 more questions CORRECTLY than they do INCORRECTLY. They answer 14 of the 16 history questions correctly. How many geography questions do they answer correctly? If you can break this down and explain simply that would be very nice. Thank you

(a) How many total questions are there?

(b) If one of the questions was answered incorrectly, then 29 were answered correctly, so 29-1 = 28 more questions were answered correctly than were answered incorrectly. What if two of the questions were answered incorrectly? What if three were? Or four? Explore until you find a value that fits with there being 24 more correct than incorrect.

(c) How many history questions were answered correctly?

(d) Then how many geography questions much also have been answered correctly?