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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
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (10％-r)/(5％-10％) = 6.722/(33.992+6.722) .
Question type: Equation
Solution:Original question:
| ( | 10 100 | − | r | ) | ÷ | ( | 5 100 | − | 10 100 | ) | = | 3361 500 | ÷ | ( | 4249 125 | + | 3361 500 | ) |
| Multiply both sides of the equation by: | ( | 5 100 | − | 10 100 | ) | , | ( | 4249 125 | + | 3361 500 | ) |
| ( | 10 100 | − | r | ) | ( | 4249 125 | + | 3361 500 | ) | = | 3361 500 | ( | 5 100 | − | 10 100 | ) |
10 100 | ( | 4249 125 | + | 3361 500 | ) | − | r | ( | 4249 125 | + | 3361 500 | ) | = | 3361 500 | ( | 5 100 | − | 10 100 | ) |
10 100 | ( | 4249 125 | + | 3361 500 | ) | − | r | ( | 4249 125 | + | 3361 500 | ) | = | 3361 500 | × | 5 100 | − | 3361 500 | × | 10 100 |
10 100 | ( | 4249 125 | + | 3361 500 | ) | − | r | ( | 4249 125 | + | 3361 500 | ) | = | 3361 10000 | − | 3361 5000 |
10 100 | ( | 4249 125 | + | 3361 500 | ) | − | r | ( | 4249 125 | + | 3361 500 | ) | = | - | 3361 10000 |
10 100 | × | 4249 125 | + | 10 100 | × | 3361 500 | − | r | ( | 4249 125 | + | 3361 500 | ) | = | - | 3361 10000 |
4249 1250 | + | 3361 5000 | − | r | ( | 4249 125 | + | 3361 500 | ) | = | - | 3361 10000 |
20357 5000 | − | r | ( | 4249 125 | + | 3361 500 | ) | = | - | 3361 10000 |
20357 5000 | − | r | × | 4249 125 | − | r | × | 3361 500 | = | - | 3361 10000 |
20357 5000 | − | 20357 500 | r | = | - | 3361 10000 |
Transposition :
| - | 20357 500 | r | = | - | 3361 10000 | − | 20357 5000 |
Combine the items on the right of the equation:
| - | 20357 500 | r | = | - | 1763 400 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
1763 400 | = | 20357 500 | r |
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 :
20357 500 | r | = | 1763 400 |
The coefficient of the unknown number is reduced to 1 :
| r | = | 1763 400 | ÷ | 20357 500 |
| = | 1763 400 | × | 500 20357 |
| = | 1763 4 | × | 5 20357 |
We obtained :
| r | = | 8815 81428 |
Convert the result to decimal form :
| r | = | 0.108255 |