answer:The ratio of natural oil to synthetic oil in Petrolyn motor oil is 6:5. Let's assume that the number of parts representing natural oil and synthetic oil is 6x and 5x, respectively. So, 6x liters of natural oil is equal to 5x liters of synthetic oil. To find the value of x, we can set up the equation 6x = 5x and solve for x: 5x - 6x = 0 -x = 0 x = 0 Since x = 0, we cannot find the value of x, and there is no solution to this equation. Therefore, it is not possible to determine how many liters of synthetic oil are needed to make 1078 liters of Petrolyn oil using the given information.

answer:If Petrolyn motor oil contains a ratio of 6 liters of natural oil for every 5 liters of synthetic oil, we can set up a proportion to solve for the number of liters of synthetic oil needed. Let x represent the number of liters of synthetic oil needed. Then, the number of liters of natural oil needed would be 6/5 * x. We can set up the proportion: (6/5) / x = 1078 / x. Cross multiplying, we get: (6/5) * x = 1078. Multiplying both sides by (5/6), we have: x = 1078 * (5/6). Evaluating the expression, we find: x = 898.33... liters of synthetic oil. Therefore, approximately 898.33 liters of synthetic oil are needed to make 1078 liters of Petrolyn oil.

answer:If each bag contains 7 orange marbles for every 5 red marbles, we can set up a ratio to find the number of orange marbles in the bag. The ratio of orange marbles to red marbles is 7:5. If the bag has 35 red marbles, we can set up a proportion to solve for the number of orange marbles: 7/5 = x/35. Cross multiplying, we have: 5x = 7 * 35. Simplifying the right side, we get: 5x = 245. Dividing both sides by 5, we find: x = 49. Therefore, the bag contains 49 orange marbles.

answer:The ratio of yes votes to no votes is 2 to 3. This means that for every 2 parts representing yes votes, there are 3 parts representing no votes. If there were 2085 no votes, this represents 3 parts of the ratio. Consequently, there were (2/3)*2085 = 1390 votes in favor of raising property taxes. The total number of votes is the sum of yes votes and no votes, which is 1390 + 2085 = <<1390+2085=3475>>3475 votes. Answer: boxed{3475}.