SOLUTION: Two foods are combined to give a total of 1600 calories and 17g of fat. The first food has 200 calories per ounce and 3g of fat per ounce, the second food has 250 calories per oun

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.