Dudley is a health-conscious student whose diet consists entirely of fried chick

Question

Dudley is a health-conscious student whose diet consists entirely of fried chicken, pizza and chocolate milkshakes. He has done some research on the internet and found the following information:

• 1 serve of fried chicken contains 20 g of fat, 45 g of protein, and no carbohy- drate.
• 1 slice of pizza contains 10 g of fat, 15 g of protein and 30 g of carbohydrate.
• 1 chocolate milkshake contains 50 g of fat, 30 g of protein and 80 g of carbo-
hydrate.
• For a balanced diet, he should consume 90 g of fat, 60 g of protein and 320 g of carbohydrate each day.

Find the number of serves of fried chicken, the number of slices of pizza and the number of milkshakes that Dudley should consume each day in order to maintain a balanced diet;
OR show that it is not possible for him to maintain a balanced diet if he continues to consume nothing other than fried chicken, pizza and milkshakes.

Explanation / Answer

Chicken = c Pizza = p Milkshake = m Fat: 90 = 20c + 10p + 50m Protein: 60 = 45c + 15p + 30m Carbs: 320 = 0c + 30p + 80m Solve for p in carbs then plug into another equation : 320 = 0c + 30p + 80m 320 = 30p + 80m Subtract 80m from both sides: 320 – 80m = 30p Divide both sides by 30: (320 – 80m)/30 = p Plug p in for protein equation: 60 = 45c + 15p + 30m 60 = 45c + 15((320 – 80m)/30) + 30m Simplify : 60 = 45c + (320 – 80m)/2) + 30m Simplify : 60 = 45c + 160 – 40m + 30m Combine terms : 60 = 45c + 160 – 10m Solve for c. Subtract 160 from both sides: -100 = 45c – 10m Add 10m to both sides: 10m -100 = 45 c Divide both sides by 45: (10m -100)/45 = c Plug in p and c into fat and solve for m: 90 = 20c + 10p + 50m 90 = 20[(10m -100)/45] + 10[(320 – 80m)/30]+ 50m Simplify: 90 = [(200m -1000)/45] + (320 – 80m)/3+ 50m Multiply everything by 45 to get rid of denominators: 4050 = 200m -1000 + 4800 – 1200m + 2250m Combine terms: 4050 = 1250m +3800 Subtract 3800 from both sides: 250 = 1250m Divide both sides by 1250: m = .2 Plug in m to carbs equation: 320 = 0c + 30p + 80(.2) 320 = 30p + 16 Subtract 16 from both sides: 304 = 30p Divide both sides by 30: p = 152/15 = 10.1333333 Plug m and p into fat equation: 90 = 20c + 10(152/15) + 50(.2) 90 = 20c + (304/3) + 10 90 = 20c + (334/3) -(64/3) = 20c C = -(16/15) Unfortunately you can’t have a negative number of pieces of fried chicken, so it is not possible to have a balanced diet eating fried chicken, pizza, and milkshakes.

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