word problems, three variables

Question

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 240 grams of carbohydrates, 332 grams of fat, and 207 grams of protein. He knows that each cup of rice provides 40 grams of carbohydrates, 0 grams of fat, and 5 grams of protein.  Each cup of tofu provides  4 grams of carbohydrates, 13 grams of fat, and 21 grams of protein. Finally, each cup of peanuts provides  26 grams of carbohydrates, 70 grams of fat, and 27 grams of protein.  How many cups of rice, tofu, and peanuts should he eat?

Answer 1

240 carbs, 332 fat, 207 protein needed

rice has 40, 0, and 5 of the 3

tofu has 4, 13, and 21

peanuts has 26, 70 and 27

per cup

40r + 4t + 26p = 240

13t + 70p = 332

5r +21t + 27p = 207

solve by substitution, elimination or matrix algebra

r=3, t=p=3

how many cups of each are needed