This Lesson (Counting calories and grams of fat in combined food) was created by by ikleyn(52908): View Source, Show About ikleyn:
Counting calories and grams of fat in combined food
Problem 1
Two foods are combined to give a total of 1600 calories and 17 g of fat. The first food has 200 calories per ounce and 3 g of fat per ounce,
the second food has 250 calories per ounce and 2 g of fat per ounce. How many ounces of each food is used?
Let x be the amount of the first food (in ounces) and y be the amount of the second food.
From the condition, you have these two equation
200*x + 250*y = 1600, (1) (counting calories)
3*x + 2*y = 17. (2) (counting grams of fat)
To solve the system, multiply eq(1) by 3 (both sides). Multiply eq(2) by 200 (both sides). The modified system is
600x + 750y = 4800, (3)
600x + 400y = 3400. (4)
Now subtract eq(4) from eq(3) (both sides). The terms with "x" will cancel each other,
and you will get a single equation for the unknown "y" only:
350y = 4800 - 3400, or
350y = 1400 ====> y = = 4.
Thus you just found that 4 ounces of the second food must be used.
To find "x", substitute the found value y= 4 into eq(2). You will get
3x + 2*4 = 17 ====> 3x = 17 - 2*4 = 9 ====> x = = 3.
Answer. 3 ounces of the first food and 4 ounces of the second food.
In the solution I used the Elimination method, so you could see how it worked.
