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Sofia is in charge of ordering ingredients for a restaurant. Only one of the meals on the restaurant's menu features shrimp, and each time that meal is ordered, the restaurant uses exactly 5 shrimp. Sofia will purchase shrimp at a price of 12.50 euros per kilogram, with approximately 42 shrimp per kilogram on average.
Sofia determined that if a total of \(\mathrm{n}\) shrimp meals are ordered at the restaurant per day on average, then a good approximation for the average daily cost to the restaurant, in euros, for the shrimp served can be found by \(\frac{\mathrm{n} \times \mathrm{p}}{\mathrm{q}}\). Select a value for \(\mathrm{p}\) and a value for g that would together create the closest approximation from among the options given for the average daily cost, in euros, to the restaurant for the shrimp served. Make only two selections, one in each column.
2
3
5
7
8
Let's organize the given information:
Let's trace the cost calculation flow:
\(\mathrm{n}\) meals → \(5\mathrm{n}\) shrimp → \(\frac{5\mathrm{n}}{42}\) kg → \(\frac{5\mathrm{n}}{42} \times 12.50\) euros
The question states we need to approximate the average daily cost using: \(\frac{\mathrm{n} \times \mathrm{p}}{\mathrm{q}}\)
Let's calculate the actual daily cost first:
Simplifying:
\(\mathrm{Cost} = \frac{5\mathrm{n} \times 12.50}{42} = \frac{62.5\mathrm{n}}{42}\)
For the formula \(\frac{\mathrm{n} \times \mathrm{p}}{\mathrm{q}}\) to equal our actual cost:
\(\frac{\mathrm{n} \times \mathrm{p}}{\mathrm{q}} = \frac{62.5\mathrm{n}}{42}\)
This means: \(\frac{\mathrm{p}}{\mathrm{q}} = \frac{62.5}{42} ≈ 1.488\)
We need to find values of p and q from the choices [2, 3, 5, 7, 8] that make \(\frac{\mathrm{p}}{\mathrm{q}}\) closest to 1.488.
Let's check key combinations that might be close to 1.488:
Comparing differences from 1.488:
With p = 3 and q = 2:
These values create the ratio \(\frac{3}{2} = 1.5\), which is the closest approximation to the actual cost coefficient of 1.488.