Member: MysticalFrost

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Let $a$ be the amount of soda contained by Bottle A and $b$ be the amount of soda contained by Bottle B. We can track the changes in amounts of soda in each bottle. First, Bottle A contains $a$ ounces, and Bottle B contains $b$ . At the next step, A is reduced by $b$ ounces, and B gains $b$ ounces, so A has $a-b$ and B has $2b$ ounces. Then, A is increased by $a - b$ ounces and $B$ is reduced by the same, so A has $2a - 2b$ and B has $3b-a$ ounces. Finally, B is increased by $3b-a$ ounces and A is decreased by the same, so A has $3a - 5b$ ounces and B has $6b - 2a$ ounces. We are given that $3a - 5b = 6b - 2a = 64$ , and we are looking for $a - b$ . Adding $3a - 5b$ to $-2a + 6b$ gives $a + b = 128$ . Adding $2a + 2b$ to $-2a + 6b$ gives $8b = 320$ , or $b = 40$ . So, $3a - 200 = 64$ , or $a = 88$ . Thus, $a - b = 88 - 40 = \boxed{48}$ ounces.

MysticalFrostFeb 14, 2022

If (4a + 3b) / (a - 2b) = 5 then 4a + 3b = 5(a - 2b) 4a + 3b = 5a - 10b 13b = a Therefore, substituting 13b for a: (a + 11b) / (a - b) = (13b + 11b) / (13b - b) = 24b / 12b = 2

MysticalFrostNov 2, 2021

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