Question

Find two consecutive integers whose sum is 67. Which of the following equations could be used to solve the problem? 2x = 67 2x + 1 = 67 2x + 2 = 67 x2 + 1= 67

Answer 1

x + (x+1) = 67 
^ ^ Integer 2 
Integer 1 

By simplifying, we get 2x + 1 = 67. Therefore, either "2x + 1 = 67" or "x2 + 1= 67" can be used. 

Your answer by solving for 'x' would be: 

2x=66 
x=33 
Therefore, (x+1)=34 

Hence, the 2 consecutive integers are 33 and 34. When added together, they equal 67, and they are consecutive (34 is 1 larger than 33). 

Answer 2

Let

x--------> the first consecutive integer

x+1-----> the second consecutive integer

we know that

$x+(x+1)=67\\2x+1=67$

therefore

the answer is

$2x+1=67$