IMAT 2016 Q7 [Bread Batches]

A bakery shop makes its own bread in batches to sell on site. Bakers always describe the quantities of other ingredients as a percentage of the weight of flour used. They will then use the percentages in the table below to calculate how much water, salt and fat are required. Today, the baker is planning to use 250 kg of flour to make White Bread.


What is the total weight of the mixture to be made?

A. 323 kg
B. 432.5 kg
C. 250 kg
D. 182.5 kg
E. 420 kg

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Simple steps to solve word problems:

  • Underline key information

  • Determine what they are trying to ask, and what you will need to solve it

  • Eliminate any non-essential information

  • Draw a picture, graph, or equation

  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.

  • Solve.

Right away we can eliminate most of the table, which is important because it gives us a narrow set of data and we will not waste our time on things not even relevant. With a calculator, this question would be very easy, but instead, we are stuck with only mental math, so I will use a trick to make this easier.

To calculate these amounts, we can break down 250kg into 100kg, 100kg, and 50kg. We will do this because they are going to help us get the percentages much easier and faster in our heads.

So we know that we are using 54% water because we are making white bread. All we have to do is take 54% of 100kg, 100kg, and 50kg and add it together.

100kg (0.54) = 54kg
100kg(0.54) = 54kg
50kg(0.54) = 27kg

Total = 54kg + 54kg + 27 kg = 135kg

100kg (0.02) = 2kg
100kg(0.02) = 2kg
50kg(0.02) = 1kg

Total = 1kg + 2kg + 2 kg = 5kg

100kg (0.17) = 17kg
100kg(0.17) = 17kg
50kg(0.17) = 8.5kg
(just take ½ of 17 because 50 is half 100 - the use of scaling is important, this is a simple case but it is a recurring skill needed in standardized testing)

Total = 17kg + 17kg + 8.5kg = 42.5kg

Total Weight (DO NOT FORGET TO ADD THE FLOUR) = flour + water + salt + fat
Total Weight = 250kg + 135kg + 42.5kg + 5kg
Total Weight = 432.5kg

\fcolorbox{red}{grey!30}{Therefore the answer is B, $432.5kg$ }

How to solve faster by answer elimination: you could have easily found this answer without the last two or three steps. First of all, we know that we start with 250kg of flour, therefore any answer equal to or less than this can immediately be eliminated. Also, when we calculate the weight, you will notice that you have XXX.5kg (0.5kg leftover), and this decimal is only found in one answer that is above 250kg.

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