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Let x be the number of sets of knives Eli could buy.
The total number of knives Eli would have if he buys x sets is 312 + 10x.
We want this number to be at least 546, so we can write the inequality:
312 + 10x ≥ 546
Subtracting 312 from both sides, we get:
10x ≥ 234
Dividing both sides by 10, we get:
x ≥ 23.4
Since the number of sets of knives must be a whole number, Eli can buy at least 24 sets of knives.