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One number is four more than another. Their sum is fourteen. Find both numbers.

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3 Answers

"One number is four more than the other."   is represented as 'x'
 
"One number is four more than the other."  is represented as 'x+4'
 
"Their sum is fourteen."  is represented as 'x+(x+4)=14'
 
"Find both numbers."
 
x+(x+4)=14
 
x+x+4=14  (add like terms)
 
2x+4=14 (isolate your 'x' variable on one side of the equality by subtracting 4 from both sides)
 
2x+4-4=14-4 
 
2x=10 (isolate your 'x' variable by dividing by 2 from both sides)
 
2x/2=10/2
 
x=5  (this is the answer to one number)
 
x+4=5+4=9 (plug in 5 for 'x' and this is the answer to four more than another)
 
Your two numbers are 5 and 9.
 
 
 
 
 
 
 
 
The question is stating that one number is "four more" than the other so this is an addition question. "More than" mean in addition to. If it was "four times more" then it would be multiplication. So by reading the question you can set up the equation as such:
 
x = one of the numbers you are looking for
 
x+4 = the other number you are looking for
 
sum = 14
 
so: (x+4) + x = 14
 
Then you solve for "X" and  add "X + 4"....then you will have both numbers.