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David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15 : 1 . He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice. How many servings can David make with the current amount of spice he has? servings

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115 : 1. He currently has 4040 grams of the spice blend, and he can go buy more if necessary. He wants to make 1010 servings, where each serving has 7575 grams of rice. Overall, David spends 4.504.50 dollars on rice.\newlineHow many servings can David make with the current amount of spice he has?\newline □\square servings

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Q. David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115 : 1. He currently has 4040 grams of the spice blend, and he can go buy more if necessary. He wants to make 1010 servings, where each serving has 7575 grams of rice. Overall, David spends 4.504.50 dollars on rice.\newlineHow many servings can David make with the current amount of spice he has?\newline □\square servings
  1. Calculate Rice Amount: First, we need to determine the total amount of rice David needs for 1010 servings, where each serving is 7575 grams of rice.\newlineCalculation: 1010 servings ×\times 7575 grams per serving =750= 750 grams of rice needed.
  2. Calculate Spice Amount: Next, we need to calculate how much spice is required for the 750750 grams of rice, using the rice-to-spice ratio of 15:115:1. Calculation: For every 1515 grams of rice, 11 gram of spice is needed. Therefore, for 750750 grams of rice, we need 750 grams15=50\frac{750 \, \text{grams}}{15} = 50 grams of spice.
  3. Check Spice Quantity: Now, we compare the amount of spice David has (4040 grams) with the amount of spice required (5050 grams) to determine if he has enough spice for 1010 servings.\newlineCalculation: David has 4040 grams of spice, but he needs 5050 grams for 1010 servings.
  4. Determine Servings with Available Spice: Since David does not have enough spice for 1010 servings, we need to find out how many servings he can make with the 4040 grams of spice he currently has.\newlineCalculation: If 11 gram of spice is needed for 1515 grams of rice, then 4040 grams of spice is enough for 40×15=60040 \times 15 = 600 grams of rice.
  5. Calculate Available Servings: Finally, we calculate how many servings of 7575 grams of rice can be made from 600600 grams of rice.\newlineCalculation: 600 grams of rice75 grams per serving=8 servings\frac{600 \, \text{grams of rice}} {75 \, \text{grams per serving}} = 8 \, \text{servings}.

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