Final answer:
To find the total quarts of the second batch of orange wax, we can use the same ratio as the first batch and apply it to the given amount of red wax. Using the ratio of yellow to red to white wax, we can solve for the missing values. The total quarts of the second batch of orange wax is 2331 quarts.
Step-by-step explanation:
To find the total quarts of the second batch of orange wax, we need to determine the ratio of yellow to red to white wax. Since the ratio remains the same as the first batch, we can use the same ratio and apply it to the given amount of red wax. If the second batch uses 777 quarts of red wax, we need to find the total amount of orange wax. Let's denote the total quarts of orange wax as O.
Using the ratio of yellow to red to white wax, let's assume the ratio is y:r:w, where y represents the amount of yellow wax, r represents the amount of red wax, and w represents the amount of white wax. From the previous batch, we know that y:r:w = 1:2:3.
Since r = 777, we can substitute this value into the ratio equation: y:777:w = 1:2:3. To find the value of y, we need to solve for it. First, simplify the ratio: y/777 = 1/2.
Multiply both sides of this equation by 777 to isolate y: y = (777 * 1)/2 = 388.5. Therefore, the total quarts of the second batch of orange wax is the sum of yellow wax (388.5 quarts), red wax (777 quarts), and white wax (388.5 * 3 = 1165.5 quarts): O = 388.5 + 777 + 1165.5 = 2331 quarts.