Answered

A bakery uses a mixture of flour and sugar in a ratio of 5:3. If they currently have 40 kilograms of this mixture and want to change the ratio to 2:5, how many kilograms of sugar should they add?



Answer :

Answer:   47.5 kg

Explanation

Let x be some positive real number

x > 0

The bakery has 5x kilograms of flour and 3x kilograms of sugar.

The ratio 5x:3x reduces to 5:3 when dividing both sides by x.

5x+3x = 40 since this is the total amount of mix they started with.

That equation solves to x = 5

  • 5x = 5*5 = 25 kilograms of flour
  • 3x = 3*5 = 15 kilograms of sugar
  • ratio = flour:sugar = 25:15 = 5:3 to help confirm things so far

Let y be the extra amount of sugar added. We go from 15 kg of sugar to 15+y kilograms. The amount of flour stays the same.

The ratio of these two items is set to 2/5.

flour/sugar = 2/5

25/(15+y) = 2/5

25*5 = 2(15+y)

125 = 30+2y

2y = 125-30

2y = 95

y = 95/2

y = 47.5 kg of sugar must be added.

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Let's check that claim.

We keep the 25 kg of flour the same.

15 kg of sugar bumps up to 15+47.5 = 62.5 kg

Then,

flour/sugar = 25/62.5 = 250/625 = (125*2)/(125*5) = 2/5

This leads to a ratio of 2:5

This proves the answer is correct.

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