SOLUTION: The difference between two numbers is 6. Ten times the smaller number is six times the larger number. What are the two numbers? We are working out of systems of equations chapte

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Question 1077749: The difference between two numbers is 6. Ten times the smaller number is six times the larger number. What are the two numbers?
We are working out of systems of equations chapter. I know how to do the work when the equations are given and know how to substitute to get my x and y. Then this came along, this word problem. I don't know how to write the equations. I believe the first one is x-y=6 but I can't see the second one in my mind. I spent hours trying to figure it out. Please help!
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
x-y=6
y is smaller, otherwise the answer would be negative
10y=6x
y=(6/10)x
x-0.6x=6
.4x=6
x=15
y=9
10 times y=6 times x=90

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

The difference between two numbers is 6. Ten times the smaller number is six times the larger number. What are the two numbers?
We are working out of systems of equations chapter. I know how to do the work when the equations are given and know how to substitute to get my x and y. Then this came along, this word problem. I don't know how to write the equations. I believe the first one is x-y=6 but I can't see the second one in my mind. I spent hours trying to figure it out. Please help!

Since you already have x - y = 6, it means that you've chosen x to be the LARGER number, and y, the SMALLER number.
With this in mind, and the fact that it's given that "Ten times the smaller number is six times the larger number," we get: 10y = 6x.
Now that you have 2 equations, I'm sure you'll be able to determine the 2 numbers.