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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 0.507/(40/Q+8.5) = 0.493/(50/Q+6.8) .
Question type: Equation
Solution:Original question:
507 1000 | ÷ | ( | 40 | ÷ | Q | + | 17 2 | ) | = | 493 1000 | ÷ | ( | 50 | ÷ | Q | + | 34 5 | ) |
| Multiply both sides of the equation by: | ( | 40 | ÷ | Q | + | 17 2 | ) | , | ( | 50 | ÷ | Q | + | 34 5 | ) |
507 1000 | ( | 50 | ÷ | Q | + | 34 5 | ) | = | 493 1000 | ( | 40 | ÷ | Q | + | 17 2 | ) |
507 1000 | × | 50 | ÷ | Q | + | 507 1000 | × | 34 5 | = | 493 1000 | ( | 40 | ÷ | Q | + | 17 2 | ) |
507 1000 | × | 50 | ÷ | Q | + | 507 1000 | × | 34 5 | = | 493 1000 | × | 40 | ÷ | Q | + | 493 1000 | × | 17 2 |
507 20 | ÷ | Q | + | 8619 2500 | = | 493 25 | ÷ | Q | + | 8381 2000 |
| Multiply both sides of the equation by: | Q |
507 20 | + | 8619 2500 | Q | = | 493 25 | ÷ | 1 | × | 1 | + | 8381 2000 | Q |
Transposition :
8619 2500 | Q | − | 8381 2000 | Q | = | 493 25 | ÷ | 1 | × | 1 | − | 507 20 |
Calculate the items on the right of the equation:
8619 2500 | Q | − | 8381 2000 | Q | = | 493 25 | − | 507 20 |
Combine the items on the left of the equation:
| - | 7429 10000 | Q | = | 493 25 | − | 507 20 |
Combine the items on the right of the equation:
| - | 7429 10000 | Q | = | - | 563 100 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
563 100 | = | 7429 10000 | Q |
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 :
7429 10000 | Q | = | 563 100 |
The coefficient of the unknown number is reduced to 1 :
| Q | = | 563 100 | ÷ | 7429 10000 |
| = | 563 100 | × | 10000 7429 |
| = | 563 | × | 100 7429 |
We obtained :
| Q | = | 56300 7429 |
Convert the result to decimal form :
| Q | = | 7.578409 |