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Some zoo monkeys are on a diet of fruit and nuts. Fruit has about 13.3g13.3\text{g} of sugar per cup and 1.36g1.36\text{g} of protein per cup. Nuts have about 4.04g4.04\text{g} of sugar per cup and 15.56g15.56\text{g} of protein per cup. Each monkey must get between 70g70\text{g} and 90g90\text{g} of sugar per day and at least 85g85\text{g} of protein per day. Which of the following daily diets fits the monkeys' needs?\newlineChoose 11 answer:\newline(A) 00 cups of fruit and 1616 cups of nuts\newline(B) 44 cups of fruit and 1.36g1.36\text{g}00 cups of nuts\newline(C) 1.36g1.36\text{g}00 cups of fruit and 44 cups of nuts\newline(D) 1616 cups of fruit and 00 cups of nuts

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Q. Some zoo monkeys are on a diet of fruit and nuts. Fruit has about 13.3g13.3\text{g} of sugar per cup and 1.36g1.36\text{g} of protein per cup. Nuts have about 4.04g4.04\text{g} of sugar per cup and 15.56g15.56\text{g} of protein per cup. Each monkey must get between 70g70\text{g} and 90g90\text{g} of sugar per day and at least 85g85\text{g} of protein per day. Which of the following daily diets fits the monkeys' needs?\newlineChoose 11 answer:\newline(A) 00 cups of fruit and 1616 cups of nuts\newline(B) 44 cups of fruit and 1.36g1.36\text{g}00 cups of nuts\newline(C) 1.36g1.36\text{g}00 cups of fruit and 44 cups of nuts\newline(D) 1616 cups of fruit and 00 cups of nuts
  1. Analyze Diet Requirements: First, let's analyze the requirements for the monkeys' diet:\newline- They need between 70g70\text{g} and 90g90\text{g} of sugar per day.\newline- They need at least 85g85\text{g} of protein per day.\newlineWe will calculate the sugar and protein content for each diet option to see which one meets these requirements.
  2. Option (A) Analysis: Option (A) proposes 00 cups of fruit and 1616 cups of nuts. Let's calculate the sugar and protein intake for this option:\newlineSugar: 00 cups of fruit ×13.3g+16\times 13.3\text{g} + 16 cups of nuts ×4.04g=0g+64.64g=64.64g\times 4.04\text{g} = 0\text{g} + 64.64\text{g} = 64.64\text{g}\newlineProtein: 00 cups of fruit ×1.36g+16\times 1.36\text{g} + 16 cups of nuts ×15.56g=0g+248.96g=248.96g\times 15.56\text{g} = 0\text{g} + 248.96\text{g} = 248.96\text{g}\newlineThis option does not meet the sugar requirement, as it is below 70g70\text{g}.
  3. Option (B) Analysis: Option (B) proposes 44 cups of fruit and 88 cups of nuts. Let's calculate the sugar and protein intake for this option:\newlineSugar: 44 cups of fruit ×13.3g+8\times 13.3\text{g} + 8 cups of nuts ×4.04g=53.2g+32.32g=85.52g\times 4.04\text{g} = 53.2\text{g} + 32.32\text{g} = 85.52\text{g}\newlineProtein: 44 cups of fruit ×1.36g+8\times 1.36\text{g} + 8 cups of nuts ×15.56g=5.44g+124.48g=129.92g\times 15.56\text{g} = 5.44\text{g} + 124.48\text{g} = 129.92\text{g}\newlineThis option meets both the sugar and protein requirements.
  4. Option (C) Analysis: Option (C) proposes 88 cups of fruit and 44 cups of nuts. Let's calculate the sugar and protein intake for this option:\newlineSugar: 88 cups of fruit ×13.3g+4\times 13.3\text{g} + 4 cups of nuts ×4.04g=106.4g+16.16g=122.56g\times 4.04\text{g} = 106.4\text{g} + 16.16\text{g} = 122.56\text{g}\newlineProtein: 88 cups of fruit ×1.36g+4\times 1.36\text{g} + 4 cups of nuts ×15.56g=10.88g+62.24g=73.12g\times 15.56\text{g} = 10.88\text{g} + 62.24\text{g} = 73.12\text{g}\newlineThis option exceeds the sugar requirement and does not meet the protein requirement.
  5. Option (D) Analysis: Option (D) proposes 1616 cups of fruit and 00 cups of nuts. Let's calculate the sugar and protein intake for this option:\newlineSugar: 1616 cups of fruit ×13.3g+0\times 13.3\text{g} + 0 cups of nuts ×4.04g=212.8g+0g=212.8g\times 4.04\text{g} = 212.8\text{g} + 0\text{g} = 212.8\text{g}\newlineProtein: 1616 cups of fruit ×1.36g+0\times 1.36\text{g} + 0 cups of nuts ×15.56g=21.76g+0g=21.76g\times 15.56\text{g} = 21.76\text{g} + 0\text{g} = 21.76\text{g}\newlineThis option greatly exceeds the sugar requirement and does not meet the protein requirement.

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