SOLUTION: The difference between two numbers is 16. Three times the larger number is 9 times the smaller. What are the numbers?

Question 220494: The difference between two numbers is 16. Three times the larger number is 9 times the smaller. What are the numbers?
Answer by likaaka(51) (Show Source): You can put this solution on YOUR website!
You must set up a system of equations. Begin by naming your variables ie.
x is one number and y is the other
If the difference (which is subtraction) of the two numbers is 16, your first equation is x-y=16
If the larger number times 3, which is x according to the first equation, is equal to 9 times the smaller, your second equation is 3x=9y
Here is your system of equations
x-y=16
3x=9y
First, solve for x in terms of y by adding y to both sides of the first equation
x-y +y=16 +y, now simplify
x=16+y
Now substitute the value of x into the second equation to solve
3(16+y)=9y, distribute the 3
48+3y=9y, move all y to one side by subtracting 3y from both sides
48+3y -3y=9y -3y, simplify
48=6y, solve for y by dividing both sides by 6
48/6=(6y)/6, simplify
y=8, so the smaller number is 8 now solve for x
x=16+y
x+16+8
x=24, the larger number is 24

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