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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 (3/31)*4.75%+(28/31)*[a*4.75%+(1-a)*4.50%] = 4.58% .
Question type: Equation
Solution:Original question:
| ( | 3 | ÷ | 31 | ) | × | 19 400 | + | ( | 28 | ÷ | 31 | ) | ( | a | × | 19 400 | + | ( | 1 | − | a | ) | × | 9 200 | ) | = | 229 5000 |
| Left side of the equation = | 3 | ÷ | 31 | × | 19 400 | + | ( | 28 | ÷ | 31 | ) | ( | a | × | 19 400 | + | ( | 1 | − | a | ) | × | 9 200 | ) |
| = | 57 12400 | + | ( | 28 | ÷ | 31 | ) | ( | a | × | 19 400 | + | ( | 1 | − | a | ) | × | 9 200 | ) |
| = | 57 12400 | + | 28 | ÷ | 31 | × | ( | a | × | 19 400 | + | ( | 1 | − | a | ) | × | 9 200 | ) |
| = | 57 12400 | + | 28 31 | ( | a | × | 19 400 | + | ( | 1 | − | a | ) | × | 9 200 | ) |
| = | 57 12400 | + | 28 31 | a | × | 19 400 | + | 28 31 | ( | 1 | − | a | ) | × | 9 200 |
| = | 57 12400 | + | 133 3100 | a | + | 63 1550 | ( | 1 | − | a | ) |
| = | 57 12400 | + | 133 3100 | a | + | 63 1550 | × | 1 | − | 63 1550 | a |
| = | 57 12400 | + | 133 3100 | a | + | 63 1550 | − | 63 1550 | a |
| = | 561 12400 | + | 7 3100 | a |
561 12400 | + | 7 3100 | a | = | 229 5000 |
Transposition :
7 3100 | a | = | 229 5000 | − | 561 12400 |
Combine the items on the right of the equation:
7 3100 | a | = | 173 310000 |
The coefficient of the unknown number is reduced to 1 :
| a | = | 173 310000 | ÷ | 7 3100 |
| = | 173 310000 | × | 3100 7 |
| = | 173 100 | × | 1 7 |
We obtained :
| a | = | 173 700 |
Convert the result to decimal form :
| a | = | 0.247143 |