498+345 is the answer but you divide the 3 for base of 9
![\bf \cfrac{4a}{3}-\cfrac{b}{4}=6 \qquad \qquad \cfrac{5a}{6}+b=13 \\\\\\ \textit{let us remove the denominators off those folks}\\ \textit{by multiplying the first one by 12, both sides}\\ \textit{and the second one by 6, both sides, thus} \\\\\\ 12\left( \cfrac{4a}{3}-\cfrac{b}{4} \right)=12(6)\implies 16a-4b=72 \\\\\\ 6\left( \cfrac{5a}{6}+b \right)=6(13)\implies 5a+6b=78](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B4a%7D%7B3%7D-%5Ccfrac%7Bb%7D%7B4%7D%3D6%0A%5Cqquad%20%5Cqquad%20%0A%5Ccfrac%7B5a%7D%7B6%7D%2Bb%3D13%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Blet%20us%20remove%20the%20denominators%20off%20those%20folks%7D%5C%5C%0A%5Ctextit%7Bby%20multiplying%20the%20first%20one%20by%2012%2C%20both%20sides%7D%5C%5C%0A%5Ctextit%7Band%20the%20second%20one%20by%206%2C%20both%20sides%2C%20thus%7D%0A%5C%5C%5C%5C%5C%5C%0A12%5Cleft%28%20%5Ccfrac%7B4a%7D%7B3%7D-%5Ccfrac%7Bb%7D%7B4%7D%20%5Cright%29%3D12%286%29%5Cimplies%2016a-4b%3D72%0A%5C%5C%5C%5C%5C%5C%0A6%5Cleft%28%20%5Ccfrac%7B5a%7D%7B6%7D%2Bb%20%5Cright%29%3D6%2813%29%5Cimplies%205a%2B6b%3D78)
![\bf \textit{now, let's do the elimination} \\\\ \begin{array}{llll} 16a-4b=72&\boxed{\times 3}\implies &48a-\underline{12b}=216\\\\ 5a+6b=78&\boxed{\times 2}\implies &10a+\underline{12b}=156\\ &&--------\\ &&58a+0\quad=372 \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%20%5Ctextit%7Bnow%2C%20let%27s%20do%20the%20elimination%7D%0A%5C%5C%5C%5C%0A%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A16a-4b%3D72%26%5Cboxed%7B%5Ctimes%203%7D%5Cimplies%20%2648a-%5Cunderline%7B12b%7D%3D216%5C%5C%5C%5C%0A5a%2B6b%3D78%26%5Cboxed%7B%5Ctimes%202%7D%5Cimplies%20%2610a%2B%5Cunderline%7B12b%7D%3D156%5C%5C%0A%26%26--------%5C%5C%0A%26%2658a%2B0%5Cquad%3D372%0A%5Cend%7Barray%7D)
solve for "a", once you get "a", plug it back into either equation to get "b"
calculate length of the sides of the rectangle and multiply then do the same with the parallelogram
Total area is 51 square units
Circumference of a white oak tree:
C = 90 in.
C = 2 r π
2 r π = 90
r · 6.28 = 90
r = 90 : 6.28
r = 14.33 in ( but it is not r in the formula )
Since the bark is 0.5 in thick: r = 14.33 - 0.5 = 13.83 in
a = r : w = 13.83 : 0.2 = 69.15 years
The widest ring is one that shows 69 years:
r = 69 · 0.2 = 13.8 in
A = r² π = 13.8² · 3.14 = 190.44 · 3.14 = 597.98 in²
Answer: The tree`s age is 69.15 years ( or 69 years and 2 months ) and the area enclosed by the outer circumference of the widest ring is 597.98 in².