danny poured 78 liters of water into containers X,Y & Z. the ratio of the volume of water in container X to the volume of water in container Y is 5:2
help me
To find the amount of water in containers X and Y, we can set up a proportion using the given ratio. The sum of the volumes of water in containers X and Y is 5 + 2 = 7 parts.
Let's use x to represent the volume of water in container X and y to represent the volume of water in container Y.
So, the proportion is:
x/y = 5/2
We can cross-multiply:
2x = 5y
Now, let's consider container Z. We know that Danny poured a total of 78 liters of water into the three containers, so the volume of water in container Z can be found by subtracting the sum of the volumes in containers X and Y from 78 liters:
z = 78 - (x + y)
Now we have a system of equations:
2x = 5y
z = 78 - (x + y)
To solve for the variables, we need one more equation. Do you have any additional information?
To find the volumes of water in each container, let's use the concept of ratios.
We know that the ratio of the volume of water in container X to the volume of water in container Y is 5:2. This means that for every 5 parts of water in container X, there are 2 parts of water in container Y.
Step 1: Calculate the total ratio.
The total ratio is obtained by adding the parts of water in container X and container Y, which gives us a total of 5 + 2 = 7 parts.
Step 2: Determine the value of each part.
To find the value of each part, we need to divide the total volume of water poured into containers X and Y, which is 78 liters, by the total number of parts (7).
Value of each part = Total volume of water / Total number of parts
Value of each part = 78 liters / 7 parts
Value of each part ≈ 11.14 liters
Step 3: Calculate the volume of water in container X and container Y.
Now that we know the value of each part, we can find the volumes of water in containers X and Y.
Volume of water in container X = Value of each part * Number of parts for X
Volume of water in container X = 11.14 liters * 5 parts
Volume of water in container X ≈ 55.7 liters
Volume of water in container Y = Value of each part * Number of parts for Y
Volume of water in container Y = 11.14 liters * 2 parts
Volume of water in container Y ≈ 22.28 liters
So, the approximate volumes of water in containers X and Y are 55.7 liters and 22.28 liters, respectively. The volume of water in container Z hasn't been provided in the question, so we cannot determine it using the given information.