SOLUTION: I have a word problem that is throwing me off: THE SUM OF TWO NUMBERS IS 18. THREE TIMES THE GREATER NUMBER EXCEEDS FOUR TIMES THE SMALLER NUMBER BY 5. FIND THE NUMBERS. I

Question 49072: I have a word problem that is throwing me off:
THE SUM OF TWO NUMBERS IS 18. THREE TIMES THE GREATER NUMBER EXCEEDS FOUR TIMES THE SMALLER NUMBER BY 5. FIND THE NUMBERS.
I know the first sentence is: x + y = 18 but how do I know which number is greater and which one is smaller? If I could just set up the equation I could solve it but I don't know how to set the equation up.
Thank you for your time.
Answer by atif.muhammad(135) (Show Source): You can put this solution on YOUR website!

THE SUM OF TWO NUMBERS IS 18. THREE TIMES THE GREATER NUMBER EXCEEDS FOUR TIMES THE SMALLER NUMBER BY 5. FIND THE NUMBERS. 
I know the first sentence is: x + y = 18 but how do I know which number is greater and which one is smaller? If I could just set up the equation I could solve it but I don't know how to set the equation up.

You are right with your first equation, x + y = 18

You asked "how do I know which number is greater and which one is smaller". The answer is, you don't. You assume the larger number to be x or vice versa or the larger number to be y and vice versa. Algebra is very flexible and you will get the right answer both ways.

Your second sentence is: THREE TIMES THE GREATER NUMBER EXCEEDS FOUR TIMES THE SMALLER NUMBER BY 5. FIND THE NUMBERS

Let's assume the greater number to be x and the smaller number to be y.

Hence we get, 3x = 4y + 5

We now have a pair of simultaneous equations!

x + y = 18...(1)

3x = 4y + 5...(2)

Manipulate (1): Make x the subject of the equation ---   x = 18 - y...(3)

Substitute (3) into (2):

3(18-y) = 4y + 5

54 - 3y = 4y + 5

7y = 49

y = 7...(4)

Substitute (4) into (3)

x = 18 - 7 = 11

Our two numbers are 11 and 7!

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