Let's break down the problem step by step to find out how many gallons of weed killer are needed to spray 9 lawns.
### Step 1: Determine the amount of weed killer per lawn
First, we need to figure out how much weed killer is used to spray one lawn.
Given:
- Total weed killer available: [tex]\( \frac{23}{4} \)[/tex] gallons
- Number of lawns that can be sprayed with this amount: [tex]\( \frac{25}{6} \)[/tex] lawns
We need to find the amount of weed killer per lawn. To do this, divide the total amount of weed killer by the total number of lawns:
[tex]\[
\text{Weed killer per lawn} = \frac{\frac{23}{4} \text{ gallons}}{\frac{25}{6} \text{ lawns}}
\][/tex]
### Step 2: Simplify the division
When dividing fractions, we multiply by the reciprocal of the divisor:
[tex]\[
\text{Weed killer per lawn} = \frac{23}{4} \times \frac{6}{25}
\][/tex]
Performing the multiplication of the fractions:
[tex]\[
\text{Weed killer per lawn} = \frac{23 \times 6}{4 \times 25} = \frac{138}{100} = 1.38 \text{ gallons per lawn}
\][/tex]
### Step 3: Determine the total amount needed for 9 lawns
Now that we know it takes 1.38 gallons to spray one lawn, we can determine how much weed killer is needed to spray 9 lawns.
[tex]\[
\text{Total amount of weed killer needed} = 1.38 \text{ gallons per lawn} \times 9 \text{ lawns}
\][/tex]
### Step 4: Perform the multiplication
[tex]\[
\text{Total amount of weed killer needed} = 1.38 \times 9 = 12.42 \text{ gallons}
\][/tex]
### Conclusion
To spray 9 lawns, it would take [tex]\( 12.42 \)[/tex] gallons of weed killer.
