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Question 163759: the difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers.
Answer by joecbaseball(37)   (Show Source):
You can put this solution on YOUR website! Let x be the bigger number and let y be the smaller number.
Then x - y = 12.
Also (2/5)x = 6 + (1/3)y.
Now, solve for either x or y in the first equation and substitute that value into the second equation. (You could also use elimination, but this is easier in this problem).
Let's solve for x....
Then x = 12 + y, and substitute this into the second equation:
(2/5)(12 + y) = 6 + y/3. Now multiply out the left hand side:
24/5 + 2y/5 = 6 + y/3. Now add the terms on the left hand side:
(24 + 2y)/5 = 6 + y/3. Now get a common denominator for the right hand side:
(24 + 2y)/5 = (18 + y)/3. You now have a ratio. Cross multiply:
3(24 + 2y) = 5(18 + y). Multiply out both sides:
72 + 6y = 90 + 5y. Now solve for y in 3 steps.
First, subtract 72 from both sides:
6y = 18 + 5y. Now subtract 5y from both sides:
y = 18. Now, substitute this value for y into either equation in the first part to get your value for x. I'll use the easy one:
x - y = 12
x - 18 = 12. Add 18 to both sides to solve for x:
x = 30.
So... your answers are x = 30 and y = 18.
You can check your answers by plugging them into the second equation also.
Good luck!
JoeC
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