Answer:
no it is not.
Step-by-step explanation:
%increase = 40% while %loss = about 28.6%
let's say it holds "x" gallons of gas.
how much is 1/3 of that? well is just (1/3)x.
how about 1/2 of that? well is just (1/2)x.
we know that
![\bf \stackrel{\textit{originally}}{\cfrac{1}{3}x}+\stackrel{\textit{gas bought}}{2}~~=~~\stackrel{\textit{sum of both}}{\cfrac{1}{2}x} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{3}x+2 \right)=6\left( \cfrac{1}{2}x \right)}\implies 2x+12=3x\implies 12=x](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Boriginally%7D%7D%7B%5Ccfrac%7B1%7D%7B3%7Dx%7D%2B%5Cstackrel%7B%5Ctextit%7Bgas%20bought%7D%7D%7B2%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7Bsum%20of%20both%7D%7D%7B%5Ccfrac%7B1%7D%7B2%7Dx%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B6%7D%7D%7B6%5Cleft%28%20%5Ccfrac%7B1%7D%7B3%7Dx%2B2%20%5Cright%29%3D6%5Cleft%28%20%5Ccfrac%7B1%7D%7B2%7Dx%20%5Cright%29%7D%5Cimplies%202x%2B12%3D3x%5Cimplies%2012%3Dx)
notice, we simply multiplied both sides by the LCD of all fractions, to just do away with the denominators.
12.57 * 4.11 = 51.6627...rounds to 51.66
Notice that
![9](https://tex.z-dn.net/?f=9%3C10%3C16%5Cimplies%5Csqrt9%3C%5Csqrt%7B10%7D%3C%5Csqrt%7B16%7D%5Cimplies3%3C%5Csqrt%7B10%7D%3C4)
and given that 10 is closer to 9, it's clear that
![\sqrt{10}](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D)
is probably closer in value to 3 then to 4. (The actual value is indeed about 3.162.)
3 out of 6 times will roll out as a multiple of 3