SOLUTION: use an algebraic approach to solve the problem. The difference of two numbers is 127. The larger number is three less than six times the smaller number. find the larger and smalle

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Question 213737: use an algebraic approach to solve the problem.
The difference of two numbers is 127. The larger number is three less than six times the smaller number. find the larger and smaller numbers.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"difference of two numbers is 127" translates to x-y=127

"The larger number is three less than six times the smaller number" means that x=6y-3


x-y=127 Start with the first equation.


6y-3-y=127 Plug in x=6y-3


5y-3=127 Combine like terms on the left side.


5y=127%2B3 Add 3 to both sides.


5y=130 Combine like terms on the right side.


y=%28130%29%2F%285%29 Divide both sides by 5 to isolate y.


y=26 Reduce.


x=6y-3 Go back to the second equation.


x=6%2826%29-3 Plug in y=26


x=156-3 Multiply


x=153 Subtract


So the two numbers are 153 and 26