To determine the minimum number of gallons needed for a goldfish tank based on the number of fish, we need to consider two components:
1. The initial size of the tank.
2. The additional water required per fish.
### Step-by-Step Solution:
1. Initial Tank Size:
- The aquarium store recommends an initial tank size of 10 gallons. This is a fixed amount that does not change regardless of the number of fish.
2. Additional Water per Fish:
- For each additional fish, the store recommends adding 0.4 gallons of water. Therefore, if there are [tex]\( x \)[/tex] fish, the additional water needed is [tex]\( 0.4 \)[/tex] gallons multiplied by [tex]\( x \)[/tex] (the number of fish).
3. Expression Setup:
- We now need to combine these two components (initial tank size and additional water per fish) into a single expression. The total number of gallons required will be the sum of the initial tank size and the additional water for [tex]\( x \)[/tex] fish.
4. Final Expression:
- The initial tank size is 10 gallons.
- The additional water needed for [tex]\( x \)[/tex] fish is [tex]\( 0.4 \times x \)[/tex] gallons.
- Combining these, we get the expression:
[tex]\[
\text{Minimum number of gallons needed} = 10 + 0.4x
\][/tex]
Thus, the expression that shows the minimum number of gallons needed for [tex]\( x \)[/tex] fish is:
[tex]\[
0.4x + 10
\][/tex]
