SOLUTION: the difference between two numbers is 18. twice the smaller number plus three times the larger is 74. what are the numbers?

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Question 30984This question is from textbook Addison Wesley Algebra
: the difference between two numbers is 18. twice the smaller number plus three times the larger is 74. what are the numbers? This question is from textbook Addison Wesley Algebra

Found 2 solutions by Nate, Paul:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
DEFINE YOUR VARIABLES:
s=smaller number
l=larger number
-------------------------------------------------------------------
DEFINE YOUR EQUATIONS:
l-s=18
3l+2s=74
-------------------------------------------------------------------
COMBINE YOUR EQUATIONS:
l-s=18
l=s+18
...........
3l+2s=74
3(s+18)+2s=74
3s+54+2s=74
5s=20
s=4
...........
l-s=18
l-4=18
l=22

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first number be x
Let the second number be y
now:
x-y=18
y=18+x (subsitution)
2x+3y=74
Use subsitution for y:
2x+3(18+x)=74
2x+3x=74-54
5x=20
x=4
y=18+4
y=22

Hence, the two numbers are 22 and 4.
Paul.