On ryan's last history test, there were two types of questions: true/false worth 2 points each and multiple choice questions worth 4 points each. if ryan earned 86 points on the test and answered 18 multiple choice questions correctly, how many true/false questions did he answer correctly?

He answered 7 true/false questions correctly

Step-by-step explanation:

True / False : 2 points each

Multiple choice: 4 points each

Assuming he answered "x" true/false questions and "y" multiple choice questions. You can write the information in the form of equations:

Points in test = 2*(true/false) + 4*(multiple choice)

86 = 2*x + 4*y

18 = y

Replacing y = 18 in the first equation:

86 = 2*x + 4*18

86 = 2*x + 72

14 = 2x

x = 7

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x