Question 49072
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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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