The 10 percent tax on 50 dollars will be 10 / 100 x 50 = <<10/100*50=5>>5 dollars.
The cost of the game and the tax will be 50 + 5 = <<50+5=55>>55 dollars.
Nina will save half of her allowance every week, or 10 / 2 = <<10/2=5>>5 dollars per week.
The total cost of the game and tax, divided by Nina's weekly savings is 55 / 5 = <<55/5=11>>11 weeks.
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