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Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (x-400-200)*(1-25%)/8000 = （x-400-450）*（1-25%）/7000 .
Question type: Equation
Solution:Original question:
Remove the bracket on the left of the equation:
The equation is transformed into :
Remove the bracket on the right of the equation:
The equation is transformed into :
Transposition :
Combine the items on the left of the equation:
Combine the items on the right of the equation:
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
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 :
The coefficient of the unknown number is reduced to 1 :
We obtained :
This is the solution of the equation.
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (x-400-200)*(1-25%)/8000 = （x-400-450）*（1-25%）/7000 .
Question type: Equation
Solution:Original question:
| ( | x | − | 400 | − | 200 | ) | ( | 1 | − | 25 100 | ) | ÷ | 8000 | = | ( | x | − | 400 | − | 450 | ) | ( | 1 | − | 25 100 | ) | ÷ | 7000 |
| Left side of the equation = | x | ( | 1 | − | 25 100 | ) | × | 1 8000 | − | 400 | ( | 1 | − | 25 100 | ) | × | 1 8000 | − | 200 | ( | 1 | − | 25 100 | ) | × | 1 8000 |
| = | x | ( | 1 | − | 25 100 | ) | × | 1 8000 | − | 1 20 | ( | 1 | − | 25 100 | ) | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | x | × | 1 | × | 1 8000 | − | x | × | 25 100 | × | 1 8000 | − | 1 20 | ( | 1 | − | 25 100 | ) | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | x | × | 1 8000 | − | x | × | 1 32000 | − | 1 20 | ( | 1 | − | 25 100 | ) | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | 3 32000 | x | − | 1 20 | ( | 1 | − | 25 100 | ) | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | 3 32000 | x | − | 1 20 | × | 1 | + | 1 20 | × | 25 100 | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | 3 32000 | x | − | 1 20 | + | 1 80 | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | 3 32000 | x | − | 3 80 | − | 1 40 | ( | 1 | − | 25 100 | ) |
| = | 3 32000 | x | − | 3 80 | − | 1 40 | × | 1 | + | 1 40 | × | 25 100 |
| = | 3 32000 | x | − | 3 80 | − | 1 40 | + | 1 160 |
| = | 3 32000 | x | − | 9 160 |
3 32000 | x | − | 9 160 | = | ( | x | − | 400 | − | 450 | ) | ( | 1 | − | 25 100 | ) | ÷ | 7000 |
| Right side of the equation = | x | ( | 1 | − | 25 100 | ) | × | 1 7000 | − | 400 | ( | 1 | − | 25 100 | ) | × | 1 7000 | − | 450 | ( | 1 | − | 25 100 | ) | × | 1 7000 |
| = | x | ( | 1 | − | 25 100 | ) | × | 1 7000 | − | 2 35 | ( | 1 | − | 25 100 | ) | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | x | × | 1 | × | 1 7000 | − | x | × | 25 100 | × | 1 7000 | − | 2 35 | ( | 1 | − | 25 100 | ) | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | x | × | 1 7000 | − | x | × | 1 28000 | − | 2 35 | ( | 1 | − | 25 100 | ) | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | 3 28000 | x | − | 2 35 | ( | 1 | − | 25 100 | ) | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | 3 28000 | x | − | 2 35 | × | 1 | + | 2 35 | × | 25 100 | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | 3 28000 | x | − | 2 35 | + | 1 70 | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | 3 28000 | x | − | 3 70 | − | 9 140 | ( | 1 | − | 25 100 | ) |
| = | 3 28000 | x | − | 3 70 | − | 9 140 | × | 1 | + | 9 140 | × | 25 100 |
| = | 3 28000 | x | − | 3 70 | − | 9 140 | + | 9 560 |
| = | 3 28000 | x | − | 51 560 |
3 32000 | x | − | 9 160 | = | 3 28000 | x | − | 51 560 |
Transposition :
3 32000 | x | − | 3 28000 | x | = | - | 51 560 | + | 9 160 |
Combine the items on the left of the equation:
| - | 3 224000 | x | = | - | 51 560 | + | 9 160 |
Combine the items on the right of the equation:
| - | 3 224000 | x | = | - | 39 1120 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
39 1120 | = | 3 224000 | 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 :
3 224000 | x | = | 39 1120 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 39 1120 | ÷ | 3 224000 |
| = | 39 1120 | × | 224000 3 |
| = | 13 | × | 200 |
We obtained :
| x | = | 2600 |