SOLUTION: Hello, I need help tonight...tried this problem at least 6 times. help The difference of two numbers is 12. Two fifths of the greater number is 6 more than one third of the less

Algebra ->  Expressions-with-variables -> SOLUTION: Hello, I need help tonight...tried this problem at least 6 times. help The difference of two numbers is 12. Two fifths of the greater number is 6 more than one third of the less      Log On


   

Question 29765: Hello, I need help tonight...tried this problem at least 6 times. help
The difference of two numbers is 12. Two fifths of the greater number is 6 more than one third of the lesser number. Find both numbers.
I know x-y=12 and 2/5x,1/3y-6, and don't know where to go from there. Please Help.
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
x-y=12
y=-12+x (subsitution)

Greater number 2x/5
Lesser number = 1y/3

Equation:
2x%2F5=6%2B1y%2F3
Multiply the whole equation by 15 to remove the fraction.
15%282x%2F5%29=15%286%2F1%29%2B15%281y%2F3%29
3%282x%29=15%286%29%2B5%28y%29
6x=90%2B5y
Subsitute
6x=90+5(-12+x)
6x=90-60+5x
x=30
y=-12+30
y=18

Check:
%282%2830%29%29%2F5=6%2B18%2F3
12=12

Hence, the two numbers are 30 and 18
Paul.