Two tanks must have a total capacity of 325 gallons. If one tank needs to be 5 times the size of the other, how many gallons should each tank hold? Round your answer to the nearest tenth.
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.
