Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, t, that he needs to prepare. Write an equation that shows how Noah can find S, the number of liters of soda water, if he knows t.

This question is obviously incomplete. Below is the complete question:

Noah's recipe for sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, t, that he needs to prepare. Write an equation that shows how Noah can find S, the number of liters of soda water, if he knows t.

Answer:

The equation for calculating the quantity of soda water, "s" is:-

s = 5t/9

Step-by-step explanation:

Before proceeding, it is important to state that this basically requires a minor knowledge of the application of ratios.

Noah usually knows the total number of litres, "t" that he needs to prepare, so all he needs to do is to derive a means for calculating the total number of litres of the soda water that he will be adding to the orange juice to arrive at the grand total "t"

Now, let us denote the number of litres of orange juice he requires at anytime as "r" and denote the number of litres of soda water that he requires as "s". The combination of these two will give a grand total of "t".

If the sparkling juice uses 4 litres of orange juice and 5 litres of soda water, it means that the sparkling juice is always in the ratio of:

4 litres of orange : 5 litres of soda

So, one sparkling juice container will probably contain 4 litres of orange + 5 litres of soda = 9 litres

r (4 litres in this case) + s (5 litres in this case) = t (9 litres in this case).

Since, the composition are always in the ratio 4:5, then

r = 4 / (4+5) * 9 = 4/9 * 9 = 4

s = 5 / (4+5) * 9 = 5/9 * 9 = 5

So, if "t" is known, we can always find or calculate "s" through the following equation:-

s = 5 / (4+5) * t = 5/9 * t = 5t/9

The equation for calculating the quantity of soda water in litres is therefore:

s = 5t/9

Step-by-step explanation:

Given:

Number of liters of soda water = S

Total number of liters of sparkling juice = t

Let a be the number of liters of orange juice

Total number of liters of sparkling juice, t = liters of orange juice + liters of soda water

= 4a + 5 * S

Since a = S,

t = 4S + 5S

t = 9S

S = t/9