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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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