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"On Thursday Bernie's dog ate 1/4 lb more dog food than she ate on Wednesday."
That means that on Wednesday, the dog ate 1/4 lb LESS that it ate on Thursday.
"On Wednesday, the dog ate 1 1/3 times the amount of food she ate on Tuesday."
That means that on Tuesday, the dog ate 1 1/3 times LESS that it ate on Wednesday.
Now start with Thursday: "If Bernie's dog ate 1 3/4 lb food on Thursday"
On Wednesday it ate 1/4 lb less that that, so on Wednesday it ate
1 3/4 - 1/4 = 1 2/4 = 1 1/2
On Wednesday it ate 1 1/2 lb.
On Tuesday it ate 1 1/3 times less than on Wednesday. Now we divide 1 1/2 by 1 1/3.
Answer: It ate 1 1/8 lb of food on Tuesday.