Question 9

Bill is trying to plan a meal to meet specific nutritional goals. He wants to prepare a meal containing rice, tofu, and peanuts that will provide 164 grams of carbohydrates, 184 grams of fat, and 128 grams of protein. He knows that each cup of rice pirovides 42 grams of carbohydrates, 0 grams of fat, and 5 grams of protein. Each cup of tofu provides 6 grams of carbohydrates, 9 grams of fat, and 17 grams of protein. Finally, each cup of peanuts provides 28 grams of carbohydrates, 74 grams of fat, and 25 grams of protein. How many cups of rice, tofu, and peanuts should he eat?
cups of rice:
cups of tofu:
cups of peanuts:

Step 1 ：Bill is trying to plan a meal to meet specific nutritional goals. He wants to prepare a meal containing rice, tofu, and peanuts that will provide 164 grams of carbohydrates, 184 grams of fat, and 128 grams of protein. He knows that each cup of rice provides 42 grams of carbohydrates, 0 grams of fat, and 5 grams of protein. Each cup of tofu provides 6 grams of carbohydrates, 9 grams of fat, and 17 grams of protein. Finally, each cup of peanuts provides 28 grams of carbohydrates, 74 grams of fat, and 25 grams of protein. How many cups of rice, tofu, and peanuts should he eat?

Step 2 ：We can represent this problem as a system of linear equations. Let \(x\) represent the number of cups of rice, \(y\) represent the number of cups of tofu, and \(z\) represent the number of cups of peanuts. We can then write the following equations based on the information given:

Step 3 ：\(42x + 6y + 28z = 164\) (for carbohydrates)

Step 4 ：\(0x + 9y + 74z = 184\) (for fat)

Step 5 ：\(5x + 17y + 25z = 128\) (for protein)

Step 6 ：We can solve this system of equations to find the values of \(x\), \(y\), and \(z\).

Step 7 ：The solution to the system of equations is \(x = 2\), \(y = 4\), \(z = 2\). This means that Bill should eat 2 cups of rice, 4 cups of tofu, and 2 cups of peanuts to meet his nutritional goals.

Step 8 ：Final Answer: \(\boxed{2}\) cups of rice, \(\boxed{4}\) cups of tofu, and \(\boxed{2}\) cups of peanuts.