Difference 5186

The unknown number was first increased by 17%, and the result was the number A. The second time, the teacher reduced the original number by 8%, resulting in number B. The difference between the numbers A and B is 50. Determine the unknown number.

Correct answer:

x =  -555.5556

Step-by-step explanation:


x - 17/100x = A
x - 8/100x = B
A-B = 50

x - 17/100·x = A
x - 8/100·x = B
A-B = 50

100A-83x = 0
100B-92x = 0
A-B = 50

Row 3 - 1/100 · Row 1 → Row 3
100A-83x = 0
100B-92x = 0
-B+0.83x = 50

Row 3 - -1/100 · Row 2 → Row 3
100A-83x = 0
100B-92x = 0
-0.09x = 50


x = 50/-0.09 = -555.55555556
B = 0+92x/100 = 0+92 · (-555.55555556)/100 = -511.11111111
A = 0+83x/100 = 0+83 · (-555.55555556)/100 = -461.11111111

A = -4150/9 ≈ -461.111111
B = -4600/9 ≈ -511.111111
x = -5000/9 ≈ -555.555556

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