They exceeded

In mines A and B, they were supposed to extract 20,000 tons of coal together. However, they exceeded their joint plan and so they extracted 133 tons more together. In mine A, they exceeded the plan by 2 percent, and in mine B, on the contrary, they extracted 1 percent less than the plan. How many tons were they supposed to extract in each mine according to the original plan and how many tons were they actually extracted?

Correct 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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