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On line Solution of Monovariate Equation：
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
Overview: 1 questions will be solved this time.Among them
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Work: Find the solution of equation 30% = (y×12.5×1.6667×0.4)/(1-y×12.5×1.6667×0.4) .
Question type: Equation
Solution:Original question:
30 100 | = | ( | y | × | 25 2 | × | 16667 10000 | × | 2 5 | ) | ÷ | ( | 1 | − | y | × | 25 2 | × | 16667 10000 | × | 2 5 | ) |
| Multiply both sides of the equation by: | ( | 1 | − | y | × | 25 2 | × | 16667 10000 | × | 2 5 | ) |
30 100 | ( | 1 | − | y | × | 25 2 | × | 16667 10000 | × | 2 5 | ) | = | ( | y | × | 25 2 | × | 16667 10000 | × | 2 5 | ) |
30 100 | × | 1 | − | 30 100 | y | × | 25 2 | × | 16667 10000 | × | 2 5 | = | ( | y | × | 25 2 | × | 16667 10000 | × | 2 5 | ) |
30 100 | × | 1 | − | 30 100 | y | × | 25 2 | × | 16667 10000 | × | 2 5 | = | y | × | 25 2 | × | 16667 10000 | × | 2 5 |
3 10 | − | 50001 20000 | y | = | y | × | 16667 2000 |
Transposition :
| - | 50001 20000 | y | − | 16667 2000 | y | = | - | 3 10 |
Combine the items on the left of the equation:
| - | 216671 20000 | y | = | - | 3 10 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
3 10 | = | 216671 20000 | y |
If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
216671 20000 | y | = | 3 10 |
The coefficient of the unknown number is reduced to 1 :
| y | = | 3 10 | ÷ | 216671 20000 |
| = | 3 10 | × | 20000 216671 |
| = | 3 | × | 2000 216671 |
We obtained :
| y | = | 6000 216671 |
Convert the result to decimal form :
| y | = | 0.027692 |