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Current location：Mathematical operation > History of Mathematical Computation > Answer
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☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation 10％ = 8％×（1/55％）×X/（1-8％×（1/55％）×X) .
Question type: Equation
Solution:Original question:
10 100 | = | 8 100 | ( | 1 | ÷ | 55 100 | ) | X | ÷ | ( | 1 | − | 8 100 | ( | 1 | ÷ | 55 100 | ) | X | ) |
| Multiply both sides of the equation by: | ( | 1 | − | 8 100 | ( | 1 | ÷ | 55 100 | ) | X | ) |
10 100 | ( | 1 | − | 8 100 | ( | 1 | ÷ | 55 100 | ) | X | ) | = | 8 100 | ( | 1 | ÷ | 55 100 | ) | X |
10 100 | × | 1 | − | 10 100 | × | 8 100 | ( | 1 | ÷ | 55 100 | ) | X | = | 8 100 | ( | 1 | ÷ | 55 100 | ) | X |
10 100 | × | 1 | − | 10 100 | × | 8 100 | ( | 1 | ÷ | 55 100 | ) | X | = | 8 100 | × | 1 | ÷ | 55 100 | × | X |
1 10 | − | 1 125 | ( | 1 | ÷ | 55 100 | ) | X | = | 8 55 | X |
1 10 | − | 1 125 | × | 1 | ÷ | 55 100 | × | X | = | 8 55 | X |
1 10 | − | 4 275 | X | = | 8 55 | X |
Transposition :
| - | 4 275 | X | − | 8 55 | X | = | - | 1 10 |
Combine the items on the left of the equation:
| - | 4 25 | X | = | - | 1 10 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
1 10 | = | 4 25 | X |
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 :
4 25 | X | = | 1 10 |
The coefficient of the unknown number is reduced to 1 :
| X | = | 1 10 | ÷ | 4 25 |
| = | 1 10 | × | 25 4 |
| = | 1 2 | × | 5 4 |
We obtained :
| X | = | 5 8 |
Convert the result to decimal form :
| X | = | 0.625 |