Question 1190069
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y = amount he is paid per week (in pounds)
4y = amount he is paid over 4 weeks total, ignoring the penalty fee
4y-2 = now accounting for the 2 pound deduction


The amount Michael is paid is 4y-2 pounds.
He finds out he's actually paid 22 pounds. 
Set those two expressions equal to one another and solve.


4y-2 = 22
4y = 22+2
4y = 24
y = 24/4
y = 6
Michael is paid 6 pounds per week


If he wasn't penalized, then he'd get paid 4y = 4*6 = 24 pounds over the four week period. 
However, he's penalized those 2 pounds to get paid 24-2 = 22 pounds instead. 
This matches with what your teacher gave you, so it confirms the answer.
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