Please help it's a maths question

Question

My manager has asked me to use 400kg worth of ingredients. Those ingredients are divided as follows: 190 kg chicken, 115 kg eggs, 95kg sugar. 10 minutes later, my manager informed me that the total of ingredients has been changed from 400kg to 280kg. How am I going to change the figures for chicken, eggs and sugar in order to be equal and add up to 280kg as the previous example when the total was 400kg? If I'm making sense then please someone answer the question and tell me how to work it out. Thanks

Answer 1

The original recipe totaled 400kg. The new recipe must total 280kg. 

The first thing we need to do is figure out what ratio of the new recipe is to the old.

 

To find a ratio, just need to make a fraction with "new" over "old".  So 280/400

 

280/400=0.70

 

This means that if we take the total amount of the original ingredients (400kg) and multiply by 0.70 we get 280kg (new total of ingredients).

 

So in order to keep the proportions of ingredients the same we just need to multiply each of the original ingredient amounts by 0.70

 

 

              OLD   x0.07   =  NEW

     

Chicken:  190   x0.07 = 133kg

Eggs:      115   x0.07 = 80.5kg

Sugar:     95    x0.07 = 66.5kg

 

Just to check : 133+80.5+66.5=280kg, exactly what we wanted.

 

 

Hope this helps let me know if you have any questions.

 

Answer 2

Hi Mahmoud

 

The best way (in my opinion) to figure out this problem is thinking about keeping the proportion of chicken, eggs and sugar the same with respect to the total amount of ingredients.

 

Let me explain myself better:

 

The original proportion of chicken was:  190Kg/400Kg

 

The original proportion of eggs was:  115Kg/400Kg

 

The original proportion of sugar was:  95Kg/400Kg

 

After the total amount of ingredients was reduced to 280Kg, the new proportions of each ingredient are:

 

New proportion of chicken is:  (c/280Kg)  where c is the weight of chicken

 

New proportion of eggs is    (e/280Kg) where e is the total weight of eggs

 

New proportion of sugar is:  (s/280Kg) where s is the weight of sugar

 

By keeping the relative proportions the same we have:

 

For chicken:   (c/280Kg) = (190Kg/400Kg)     or  c = (190Kg/400Kg)*280Kg = 133Kg

 

For eggs: (e/280Kg) = (115Kg/400Kg)   or   e = (115Kg/400Kg)*280Kg = 80.5Kg

 

For sugar: (s/280Kg) = (95Kg/400Kg)   or    s =(95Kg/400Kg)*280Kg = 66.5

 

Then, the new ingredients are distributed as follows:

 

Total amount of chicken      =    133 Kg

Total amount of eggs          =    80.5 Kg

Total amount of sugar         =    66.5 Kg

                                             ------------

Total amount of ingredients       280 Kg

 

Answer 3

If the ingredients are to be in the same proportion, when the total was changed from 400 kg to 280 kg, the new total was reduced  to 70% of the original.

 

Take 70% of each of the ingredients:

Chicken: .7  * 190 = 133 kg

Eggs: .7 * 115 = 80.5 kg

Sugar: .7 * 95 = 66.5 kg

Answer 4

Total ingredients have been reduced by a factor of 280/400= 0.7

All the ingredients should also be reduced by the same factor

Chicken - 190 x 0.7 = 133 kg

Eggs - 115 x 0.7 = 80.5 kg

Sugar - 95 x 0.7 = 66.5 kg

:)