Question 1101630
.
<pre>
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 = {{{1400/350}}} = 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 = {{{9/3}}} = 3.


<U>Answer</U>.  3 ounces of the first food and 4 ounces of the second food.
</pre>


In the solution I used the Elimination method, so you saw how it worked.