SOLUTION: I NEED TO SET UP AN EQUATION FOR THIS WORD PROBLEM: THE SUM OF TWO NUMBERS IS 18. THREE TIMES THE GREATER NUMBER EXCEEDS FOUR TIMES THE SMALLER NUMBER BY 5. FIND THE NUMBERS.

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Question 14450: I NEED TO SET UP AN EQUATION FOR THIS WORD PROBLEM:
THE SUM OF TWO NUMBERS IS 18. THREE TIMES THE GREATER NUMBER EXCEEDS FOUR TIMES THE SMALLER NUMBER BY 5. FIND THE NUMBERS.
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
let the smaller number be x and greater number be y.
sum of numbers = x+y = 18.......(1)
three times the greater number = 3*y
four times the smaller number = 4*x
three times the greater number exceeds four times the smaller number by 5
hence 3*y-4*x=5
-4*x+3*y=5 .........(2).we have 2 unknowns.let us eliminate one unknown say x.for this multiply eqn.(1) with 4 and add to eqn.(2).
eqn.(1)*4 gives us ....4*x+4*y=4*18=72.......(3)adding to eqn.(2)
-4*x+3*y=5......(2) we get
4*y+3*y=7*y=72+5=77
y=77/7=11 substituting in 1 we get
x+11=18 or x=18-11=7