SOLUTION: The sum of two number is 40.When the greater number is divided by the smaller,the result is one more than one-half thd smaller number.Find the number.

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Question 1131050: The sum of two number is 40.When the greater number is divided by the smaller,the result is one more than one-half thd smaller number.Find the number.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x%3Cy

This is the system according to description. This is literally what the description says:
system%28x%2By=40%2Cy%2Fx=x%2F2%2B1%29

substituting y=40-x into the rational equation,
%2840-x%29%2Fx=x%2F2%2B1
2x%2840-x%29%2Fx=2x%28x%2F2%29%2B2x%2A1
80-2x=x%5E2%2B2x, simplifying to ,...

highlight_green%28x%5E2%2B4x-80=0%29

Use the general formula solution for quadratic equation to find x and each corresponding y. You do that further arithmetic.
.
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x=-2-2%2Asqrt%2821%29 and y=42%2B2%2Asqrt%2821%29
OR
x=-2%2B2%2Asqrt%2821%29 and y=42-2%2Asqrt%2821%29