SOLUTION: Please help me solve my son's word problem. The sum of two number is 63. Three times the larger number is 14 more than two times the smaller number. What are the numbers? Thank

Algebra ->  Equations -> SOLUTION: Please help me solve my son's word problem. The sum of two number is 63. Three times the larger number is 14 more than two times the smaller number. What are the numbers? Thank      Log On


   

Question 29356: Please help me solve my son's word problem. The sum of two number is 63. Three times the larger number is 14 more than two times the smaller number. What are the numbers? Thank you.
Found 2 solutions by longjonsilver, askmemath:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let smaller number be x
Let larger number be y

their sum is 63 --> x+y=63
three times the larger is 14 more than two times the smaller -->
3y = 14 + 2x
--> 3y-2x = 14

2 equations, 2 unknows...you can solve them.

Answers are: x=35 and y = 28

i cannot see a mistake in my working and yet x is the larger number, yet is defined as the smaller... is the question "three times the smaller..."?

jon.

Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 2 numbers = X and Y
Given X+Y = 63
Let the Larger Number = X
3X = 2Y+14
X+Y = 63
multiply both sides with 3
3X+3Y = 63*3
But we already know that 3X = 2Y+14
2Y+14+3Y= 189
5y+14 = 189
Subtracting 14 on both sides
5Y = 189-14
5Y = 175
Dividing by 5 on both sides
Y = 35
X = 63-35 = 28
Ok, I've looked at this a number of times and for the life of me I cannot figure out where I am wrong since X is supposed to be the larger number and yet I get the value of X smaller than Y.