Answers:
Larger bottle = 44 gallons
Smaller bottle = 33 gallons
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Step-by-step explanation:
L = capacity of larger bottle
S = capacity of smaller bottle
Capacities are in gallons
We're told the ratio of these capacities is 4 to 3, meaning L/S = 4/3. Note how L goes first on top since 4 is the first number and it's larger than 3.
Cross multiply to get 3L = 4S. We can solve for S to get S = 3L/4.
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We're also told that the larger bottle has 11 more gallons than the smaller one, so,
Larger = Smaller + 11
L = S+11
L = (3L/4) + 11 .... plug in S = 3L/4
4L = 4*(3L/4) + 4*11 ... multiply every term by 4
4L = 3L + 44 .... the fraction goes away afterward
4L-3L = 44 .... subtract 3L from both sides
L = 44
The larger bottle can hold 44 gallons
S = 3L/4
S = 3*44/4
S = 3*11
S = 33
The smaller bottle can hold 33 gallons
Note that L-S = 44-33 = 11 to show there's an 11 gallon difference between the larger and smaller bottles. We can also see that L/S = 4/3 is also true because 44/33 = 4/3. This confirms our answers.