They exceeded

Mines A and B were supposed to extract 20,000 tonnes of coal together. However, they exceeded their joint plan and extracted 133 tonnes more in total. Mine A exceeded its plan by 2 percent, while mine B extracted 1 percent less than its plan. How many tonnes was each mine supposed to extract according to the original plan, and how many tonnes did each actually extract?

Final Answer:

a =  11100
b =  8900
a1 =  11322 t
b1 =  10989 t

Step-by-step explanation:


a+b = 20000
1.02a + 0.99 b = 20000 + 133

a+b = 20000
1.02·a + 0.99·b = 20000 + 133

a+b = 20000
1.02a+0.99b = 20133

Pivot: Row 1 ↔ Row 2
1.02a+0.99b = 20133
a+b = 20000

Row 2 - 1/1.02 · Row 1 → Row 2
1.02a+0.99b = 20133
0.03b = 261.76


b = 261.76470589/0.02941176 = 8900.00000064
a = 20133-0.9900000000016b/1.02 = 20133-0.99 · 8900.00000064/1.02 = 11099.99999936

a = 11099.999999
b = 8900.000001

Our linear equations calculator calculates it.
a1=1.02a=1.02 11100=11322 t
b1=0.99a=0.99 11100=10989 t



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