Certainly! Let's solve this problem step by step.
### Understanding the Given Ratio
We are given the ratio of gallons of water to cups of cleaner as:
[tex]\[ 4 : \frac{1}{3} \][/tex]
This means that for every [tex]\(\frac{1}{3}\)[/tex] cup of cleaner, we need 4 gallons of water.
### Finding the Ratio per One Cup of Cleaner
First, let's determine how many gallons of water are needed for 1 cup of cleaner.
1. We start by finding how many [tex]\(\frac{1}{3}\)[/tex] cups of cleaner fit into 1 cup:
[tex]\[
\text{Number of } \frac{1}{3} \text{ cups in 1 cup} = \frac{1}{\frac{1}{3}} = 3
\][/tex]
2. Since the ratio scenario of 4 gallons is based on [tex]\(\frac{1}{3}\)[/tex] cup of cleaner, we need to multiply the 4 gallons by the number of [tex]\(\frac{1}{3}\)[/tex] cups in 1 cup:
[tex]\[
\text{Gallons of water per cup of cleaner} = 4 \times 3 = 12
\][/tex]
So, to maintain the same ratio, we need 12 gallons of water for every 1 cup of cleaner.
### Answer
If you have 1 cup of cleaner and want to maintain the ratio of [tex]\(4 : \frac{1}{3}\)[/tex], you will need 12 gallons of water to mix with the 1 cup of cleaner.
Hence, the detailed result is:
- The ratio of gallons of water to cups of cleaner is 12.
- Therefore, for 1 cup of cleaner, you will need 12 gallons of water.
