Let's break down the problem step by step:
1. Define Variables:
- Let the capacity of the smaller tank be [tex]\( x \)[/tex] gallons.
- Since the larger tank is 5 times the size of the smaller tank, its capacity will be [tex]\( 5x \)[/tex] gallons.
2. Set Up the Equation:
- The total capacity of both tanks is given as 325 gallons.
- Therefore, we can set up the equation:
[tex]\[
x + 5x = 325
\][/tex]
- Simplify the equation:
[tex]\[
6x = 325
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], divide both sides of the equation by 6:
[tex]\[
x = \frac{325}{6}
\][/tex]
4. Calculate [tex]\( x \)[/tex]:
- Doing the division:
[tex]\[
x \approx 54.2
\][/tex]
- So, the capacity of the smaller tank is approximately 54.2 gallons.
5. Calculate the Capacity of the Larger Tank:
- Since the larger tank is 5 times the capacity of the smaller tank:
[tex]\[
5x \approx 5 \times 54.2 = 271.0
\][/tex]
6. Round the Capacities:
- The capacities in gallons are already rounded to the nearest tenth.
Therefore, the smaller tank should hold approximately 54.2 gallons, and the larger tank should hold approximately 270.8 gallons.
