Question 223553: 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 drj(1380) (Show Source):
You can put this solution on YOUR website! 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
Step 1. Let x be one smaller number
Step 2. Let y be the larger number.
Step 3. Then -x+y=12 since the difference of two numbers is 12.
Step 4. since two fifths of the greater number is six more than one third of the lesser number
Multiply by 15 to get rid of the denominators.
Subtract 5x from both sides of the equation
Step 5. So here's our system of linear equations From Steps 3 and 4:
Solve: We'll use substitution. After moving 1*y to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that y=30. Since , x=18.
Answer: .
Step 6. The numbers are 18 and 30.
I hope the above steps were helpful.
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