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[ 1/1 Equation]
Work: Find the solution of equation (100-t)/(t-37) = (212-t)/(t-100) .
Question type: Equation
Solution:Original question:| | ( | 100 | − | t | ) | ÷ | ( | t | − | 37 | ) | = | ( | 212 | − | t | ) | ÷ | ( | t | − | 100 | ) |
| Multiply both sides of the equation by: | ( | t | − | 37 | ) | , | ( | t | − | 100 | ) |
| | ( | 100 | − | t | ) | ( | t | − | 100 | ) | = | ( | 212 | − | t | ) | ( | t | − | 37 | ) |
Remove a bracket on the left of the equation:：
| | 100 | ( | t | − | 100 | ) | − | t | ( | t | − | 100 | ) | = | ( | 212 | − | t | ) | ( | t | − | 37 | ) |
Remove a bracket on the right of the equation:：
| | 100 | ( | t | − | 100 | ) | − | t | ( | t | − | 100 | ) | = | 212 | ( | t | − | 37 | ) | − | t | ( | t | − | 37 | ) |
Remove a bracket on the left of the equation:
| | 100 | t | − | 100 | × | 100 | − | t | ( | t | − | 100 | ) | = | 212 | ( | t | − | 37 | ) | − | t | ( | t | − | 37 | ) |
Remove a bracket on the right of the equation:：
| | 100 | t | − | 100 | × | 100 | − | t | ( | t | − | 100 | ) | = | 212 | t | − | 212 | × | 37 | − | t | ( | t | − | 37 | ) |
The equation is reduced to :
| | 100 | t | − | 10000 | − | t | ( | t | − | 100 | ) | = | 212 | t | − | 7844 | − | t | ( | t | − | 37 | ) |
Remove a bracket on the left of the equation:
| | 100 | t | − | 10000 | − | t | t | + | t | × | 100 | = | 212 | t | − | 7844 | − | t | ( | t | − | 37 | ) |
Remove a bracket on the right of the equation:：
| | 100 | t | − | 10000 | − | t | t | + | t | × | 100 | = | 212 | t | − | 7844 | − | t | t | + | t | × | 37 |
The equation is reduced to :
| | 200 | t | − | 10000 | − | t | t | = | 249 | t | − | 7844 | − | t | t |
the solutions is:
t1=-44
There are 1 solution(s).
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