SOLUTION: I want to know the meaning of the word "exceeds" in math algebra word sums. My question is "the sum of two numbers is 18. Three times the greater number exceeds four times the sm

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Question 1066221: I want to know the meaning of the word "exceeds" in math algebra word sums. My question is "the sum of two numbers is 18. Three times the greater number exceeds four times the smaller number by 5. Find the number."Please help me!!!
My solution so far:
3x + 5 = 4x ???
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
"the sum of two numbers is 18" means that we have two unknown numbers, call them x and y for now, that add up to 18

so

Solve for y to get (I subtracted x from both sides)

------------------------------------------------

Let's say that x is the greater number. So x > y.

"Three times the greater number exceeds four times the smaller number by 5"
translates to
"three times x is equal to (4 times y) plus 5"
which creates this equation


-----------------------------------------------------------------
We'll plug the equation into the second equation we just got. Then solve for x.



Replace y with 18-x





Add 4x to both sides



Divide both sides by 7



One of the numbers, the larger number, is 11.

Use this to find y



The other number is 7

In summary, the two numbers are 7 and 11.

Side note: The instruction "find the number" is too vague since it previously mentions two numbers.
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!
I want to know the meaning of the word "exceeds" in math algebra word sums. My question is "the sum of two numbers is 18. Three times the greater number exceeds four times the smaller number by 5. Find the number."Please help me!!!
My solution so far:
3x + 5 = 4x ???
"Exceeds" means greater, or more than. For the last sentence, I think you mean, "Find the numbers."



Let the smaller number be S

Then LARGER number is: 18 - S (If they sum to 18, and one is S, the other MUST be 18 - S)

Three times the GREATER/LARGER number means: 3(18 - S) = 54 - 3S

Four times the SMALLER number means: 4S 

Since 3 times the larger EXCEEDS 4 times the smaller by 5, we can say that: 54 - 3S = 4S + 5 (This is because the LEFT SIDE is greater

than the right side by 5, so we can either SUBTRACT 5 from the left, or ADD 5 to the right side). I chose to ADD 5 to the right side. 



 54 - 3S =  4S + 5 ------ Bringing down the equation

    + 3S  + 3S     ------ Adding 3S to both sides of equation

      54 =  7S + 5

     - 5       - 5 ------ Subtracting 5 on both sides 

      49 = 7S

S, or smaller number = 

Larger number =  

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