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A restaurant makes smoothies in batches of 5.6 litres.
The smoothies are made from ice cream and a mixed fruit juice in the ratio 4: 3.
45% of the juice is grape juice.
Work out the maximum number of batches of smoothie that can be made from 54 litres of grape juice.



Answer :

chibabykalu16

Answer:

50

Step-by-step explanation:

Given:

  • 5.6 litres per batch
  • Ratio of 4:3

To determine the number of batches reproducible from 54 litres of grape juice, we need to find the amount of grape juice per batch.

[tex] \rightarrow \sf ratio = 4 : 3[/tex]

We find the value of each ingredients in litres per batch

[tex] \sf \text{ice cream} = \frac{5.6 \times 4}{7} = 3.2 \: \text{litres}[/tex]

[tex] \sf \text{fruit juice (both grape juice} \\ \sf = \frac{5.6 \times 3}{7} = 2.4 \: \text{litres}[/tex]

Now we've found these values let look for the value for 45% grape juice in the fruit juice

[tex] \sf grape \: juice = 2.4 \times 0.045 [/tex]

[tex] \sf = 1.08 \: litres[/tex]

Lastly, we would divide 54 litres by the 45% grape juice value earlier

[tex] \rightarrow \sf number \: of \: batches = \frac{54}{1.08} [/tex]

[tex] \sf \boxed{ \sf 50}[/tex]

dashataran

Answer:

50

Step-by-step explanation:

Let the amount of icecream be 4x litres and the amount of mixed fruit juice is 3x litres in each batches of smoothies.

Now the equation for one batch is:

4x + 3x = 5.6

or, 7x = 5.6

or, x = 0.8

Thus in one batch of 5.6 litres:

  • Amount of icecream = 4x = 4(0.8) = 3.2 litres
  • Amount of mixed fruit juice = 3x = 3(0.8) = 2.4 litres

Now,

Amount of grape juice in one batch = 45% of mixed fruit juice = 45% x 2.4

= 1.08 litres

That means,

  • Number of batches prepared by 1.08 litres grape juice = 1
  • or, Number of batches prepared by 1 litre grape juice = [tex]\dfrac{1}{1.08}[/tex]
  • Number of batches prepared by 54 litres grape juice = [tex]\dfrac{1}{1.08}\times 54=50[/tex]

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