Four pounds of onions costs the same as 2 pounds of string beans. At the same time, 1 pound of string bean costs 3 times as much as a pound of potatoes, while 1 pound of onions costs 4 cents less than 2 pounds of potatoes. What is the total cost (without tax) of 1 pound of each of the vegetables?

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Denote Costs of Items:  Let's denote the cost of 1 pound of onions as O, 1 pound of string beans as S, and 1 pound of potatoes as P. We know that 4 pounds of onions cost the same as 2 pounds of string beans, so: 4O = 2S From this, we can find S in terms of O: S = 2O Equating and Solving:  Next, we know that 1 pound of string beans costs 3 times as much as 1 pound of potatoes: S = 3P Since we found S = 2O, we can equate and solve for O in terms of P: 2O = 3P O = 1.5P Finding Prices:  We also know that 1 pound of onions costs 4 cents less than 2 pounds of potatoes: O = 2P - 0.04 Substituting O = 1.5P from the previous step: 1.5P = 2P - 0.04 0.5P = 0.04 P = 0.08 Calculating Final Values:  Now that we have P, we can find O and S: O = 1.5P = 1.5 * 0.08 = 0.12 S = 3P = 3 * 0.08 = 0.24

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