You are making sandwiches again. This time, one double-decker sandwich consists

Question

You are making sandwiches again. This time, one double-decker sandwich consists of 3 slices of bread, 2 chicken slices, and 4 tomato slices. Suppose that you have 3.15 kg of slices of bread, 1.52 kg of chicken slices, and 1.92 kg of tomato slices.You also know that a dozen slices of bread weigh 360 g, a dozen slices of chicken weigh 240 g, and a dozen slices of tomato weigh 144 g. (One dozen is 12). (a) What is the maximum number of complete sandwiches you can make with the quantities you have available? (b) Which ingredient is the limiting one? (c) What is the mass (in grams) of one sandwich?

Explanation / Answer

Given the weight of 12 slices of bread = 360 g

Hence the weight of 1 slice of bread = 360 g / 12 = 30 g

weight of 12 slices of chicken = 240 g

Hence the weight of 1 slice of chicken = 240 g / 12 = 20 g

weight of 12 slices of tomato = 144 g

Hence the weight of 1 slice of tomato = 144 g / 12 = 12 g

Given one double-decker sandwich consists of 3 slices of bread, 2 chicken slices, and 4 tomato slices.

(c): Hence mass of one sandwich = 3*30 g + 2*20 g + 4*12 g = 178 g (answer)

Given total mass of bread slices = 3.15 Kg = 3150 g

Hence total slices of bread available = 3150 g x (1 slice bread / 30 g) = 105 slices bread

We can use 105 bread slices to make 105 / 3 = 35 sandwiches

total mass of chicken slices = 1.52 Kg = 1520 g

Hence total slices of chicken available = 1520 g x (1 slice chicken / 20 g) = 76 slices chicken

We can use 76 chichen slices to make 76 / 2 = 38 sandwiches

total mass of tomato slices = 1.92 Kg = 1920 g

Hence total slices of tomato available = 1920 g x (1 slice bread / 12 g) = 160 slices tomato

We can use 160 bread slices to make 160 / 4 = 40 sandwiches

(b) Since least number of sandwiches can be made out of bread, bread is the limiting one (answer)

Hence the maximum number of sandwiches that we can make = 35 (answer)

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