To make a jug of lemonade, Siva used 3 cups of sugar syrup for every 5 cups of lemon juice.
1. What proportion of the jug of lemonade was the number of cups of sugar syrup?
The proportion of the jug of lemonade that was the number of cups of sugar syrup is:
3 cups of sugar syrup / (3 cups of sugar syrup + 5 cups of lemon juice)
Simplifying:
3/8 or 0.375
So, 37.5% of the jug of lemonade was the number of cups of sugar syrup.
To find the proportion of the jug of lemonade represented by the number of cups of sugar syrup, we need to determine the ratio of sugar syrup to the total volume of lemonade.
Given that Siva used 3 cups of sugar syrup for every 5 cups of lemon juice, we can assume that the total volume of lemonade is the sum of sugar syrup and lemon juice.
Let's denote the number of cups of sugar syrup as x and the number of cups of lemon juice as y.
According to the given ratio, we have the following equation:
3/5 = x/y
To find the proportion of the jug of lemonade represented by the number of cups of sugar syrup, we need to determine x / (x + y).
Let's solve for x / (x + y) using the given ratio:
3/5 = x/y
Cross-multiplying, we get:
5x = 3y
Rearranging the equation, we have:
x = (3/5)y
Substituting this value of x into x / (x + y), we get:
(3/5)y / ((3/5)y + y)
(3y/5) / ((3y+5y)/5)
(3y/5) / (8y/5)
(3y/5) * (5/8y)
(3/8)
Therefore, the proportion of the jug of lemonade represented by the number of cups of sugar syrup is 3/8.
To find the proportion of the jug of lemonade that was the number of cups of sugar syrup, we need to calculate the ratio of cups of sugar syrup to the total amount of lemonade.
Given that Siva used 3 cups of sugar syrup for every 5 cups of lemon juice, we can assume that the ratio of sugar syrup to lemon juice remains constant. Therefore, we can use this ratio to calculate the proportion of sugar syrup in the jug of lemonade.
Let's assume that the jug of lemonade contains x cups of lemon juice. Since Siva used 5 cups of lemon juice for every 3 cups of sugar syrup, the ratio of lemon juice to sugar syrup is 5:3.
We can set up a proportion using this ratio:
5 cups of lemon juice / 3 cups of sugar syrup = x cups of lemon juice / y cups of sugar syrup
Cross-multiplying gives us:
5y = 3x
Now, to find the proportion of the jug of lemonade that is the number of cups of sugar syrup (in relation to the lemon juice), we need to divide the amount of sugar syrup (y) by the total amount of lemonade (x + y):
Proportion = y / (x + y)
Substituting 3x for 5y:
Proportion = 3x / (x + 3x)
Simplifying further:
Proportion = 3x / (4x)
Simplifying the equation gives us:
Proportion = 3/4
Therefore, the proportion of the jug of lemonade that is the number of cups of sugar syrup is 3/4 or 0.75.