EASY I just haven't done algebra in a while so I forgot lol. Two water bottles have capacities in the ratio 4 to 3. The larger bottle has 11 more gallons than the smaller one. How much water will the larger and smaller bottle hold?

Answers:

Larger bottle = 44 gallons

Smaller bottle = 33 gallons

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.

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.

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