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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.

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Verified Answer :

chibabykalu16 chibabykalu16 · Answer 1 · 2024-05-26T02:33:49-04:00

Answer:

50

Step-by-step explanation:

Given:

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

\(\rightarrow \sf ratio = 4 : 3\)

We find the value of each ingredients in litres per batch

\(\sf \text{ice cream} = \frac{5.6 \times 4}{7} = 3.2 \: \text{litres}\)

\(\sf \text{fruit juice (both grape juice} \\ \sf = \frac{5.6 \times 3}{7} = 2.4 \: \text{litres}\)

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

\(\sf grape \: juice = 2.4 \times 0.045\)

\(\sf = 1.08 \: litres\)

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

\(\rightarrow \sf number \: of \: batches = \frac{54}{1.08}\)

\(\sf \boxed{ \sf 50}\)

dashataran dashataran · Answer 2 · 2024-05-26T02:43:10-04:00

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:

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 = \(\dfrac{1}{1.08}\)
Number of batches prepared by 54 litres grape juice = \(\dfrac{1}{1.08}\times 54=50\)