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.

Click here to see ALL problems on Miscellaneous Word Problems

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