SOLUTION: A certain diet consists of dishes A, B and C. Each serving of A has 1 gram of fat, 2 grams of carbohydrate and 4 grams of protein. Each serving of B has 2 grams of fat, 1 gram of

Question 1030960: A certain diet consists of dishes A, B and C. Each serving of A has 1 gram of fat, 2 grams of carbohydrate and 4 grams of protein. Each serving of B has 2 grams of fat, 1 gram of carbohydrate and 3 grams of protein. Each serving of C has 2 grams of fat, 4 grams of carbohydrate and 3 grams of protein. The diet allows 15 grams of fat, 24 grams of carbohydrates and 30 grams of protein. How many servings of dish ca be eaten.
Need three linear equations.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of servings of dish A allowed
Let = number of servings of dish B allowed
Let = number of servings of dish C allowed
-----------------------------------------
Grams of fat allowed:
(1)
Grams of carbs allowed:
(2)
Grams of protein allowed:
(3)
------------------------
Multiply both sides of (1) by
and subtract (2) from (1)
(1)
(2)
-------------------------

--------------
Plug this result into (1) and (3)
(1)
(1)
and
(3)
(3)
---------------------------
Multiply both sides of (1) by
and subtract (3) from (1)
(1)
(2)
----------------------

--------------
Plug these results back into (1)
(1)
(1)
(1)
---------------
3 servings of dish A are allowed
2 servings of dish B are allowed
4 servings of dish C are allowed
---------------------------
check:
(1)
(1)
(1)
(1)
OK -you can check (2) and (3)
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