Lesson Counting calories and grams of fat in combined food
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<H2>Counting calories and grams of fat in combined food</H2> <H3>Problem 1</H3>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? <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 could see how it worked. 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