Question

To make lemonade, i use a ratio of $7$ parts water to $1$ part lemon juice. if i want to make a gallon of lemonade, and there are four quarts in a gallon, how many quarts of water do i need? write your answer as a proper or improper fraction.

Answer 1

3.5 gallons of water.

Explanation:

According to the problem, water and lemon have the ratio 7:1, 7 parts of water per 1 part of lemon.

Also, we know that one gallon have four quarts, and we want to make 1 gallon of lemonade. So, the amount of water would be
`x`, because the question is about water, and the amount of lemonade would be
`4 \ quarts - x`, because it would be the difference between the total 4 quarts (1 gallon) and the amount of water.

Now, using the ratios, we have:

`(7 \ water)/(1 \ lemon)=(x \ water)/(4 - x \ lemon) \\28-7x=x\\7x+x=28\\8x=28\\x=(28)/(8)=3.5`

Therefore, the amount of water needed is 3.5 gallons, and 0.5 gallons of lemon.

Answer 2

In order to solve this problem, we need our knowledge on ratio and proportion for us to set up an equation. A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. We do as follows:

7 parts water / 1 part lemon = 4 quarts - x / x

where x is the quarts lemon needed

Solving for x,

x = 0.5
water needed = 4-x = 3.5 quarts water is needed