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To find the price per cup, we need to know the number of cups in the 2-quart carton.
There are 4 cups in 1 quart.
So, 2 quarts will have 2 x 4 = <<2*4=8>>8 cups.
Therefore, the price per cup is $1.76/8 = $<<1.76/8=0.22>>0.22.
The price per cup is $0.22.