two tanks are each partially filled with 96 gallons of water, as shown in the illustration. tank a is…
two tanks are each partially filled with 96 gallons of water, as shown in the illustration. tank a is $\frac{4}{5}$ full, and tank b is $\frac{2}{3}$ full. what is the maximum amount of water that can be held in both tanks together?\na 128 gallons\nb 192 gallons\nc 256 gallons\nd 264 gallons
Answer
Explanation:
Step1: Find capacity of Tank A
Let capacity of Tank A be $x$. Since it is $\frac{4}{5}$ full and has 96 gallons, we have $\frac{4}{5}x = 96$. Solving for $x$ gives $x=96\div\frac{4}{5}=96\times\frac{5}{4}=120$ gallons.
Step2: Find capacity of Tank B
Let capacity of Tank B be $y$. Since it is $\frac{2}{3}$ full and has 96 gallons, we have $\frac{2}{3}y = 96$. Solving for $y$ gives $y = 96\div\frac{2}{3}=96\times\frac{3}{2}=144$ gallons.
Step3: Calculate total capacity
Total capacity of both tanks is $120 + 144=264$ gallons.
Answer:
D. 264 gallons