Danny poured 78 liters of water into containers X, Y, and Z. The ratio of the volume of water in Container X to the volume of water in Container Y is 5 : 2. The ratio of the volume of water in Container Y to the volume of water in Container Z is 8 : 11.
a) How much water was poured into Container X
b) How much more water was poured into Container X than Container Z?
x+y+z = 78
x/y = 5/2
y/z = 8/11
(x,y,z) = (40,16,22)
x-z = 18
the name not rod it's james
To find the volume of water in each container, we need to use the given ratios.
Let's assign variables:
Volume of water in Container X = 5x
Volume of water in Container Y = 2x
Volume of water in Container Z = y
We know that Danny poured a total of 78 liters of water into the containers.
a) The volume of water in Container X is 5x. We need to find the value of x.
Since the volume of water in all three containers combined is 78 liters, we can set up the equation:
5x + 2x + y = 78
Combining like terms, we have:
7x + y = 78
Since we have another equation relating the volumes of Y and Z, let's use it to solve for x.
b) The ratio of the volume of water in Container Y to the volume of water in Container Z is 8:11.
We can write this as:
2x / y = 8 / 11
To simplify this equation, we can cross-multiply:
2x * 11 = 8 * y
22x = 8y
Now, let's substitute the value of y from this equation into the earlier equation:
7x + y = 78
7x + (22x / 8) = 78
To get rid of the fraction, let's multiply both sides of the equation by 8:
8 * (7x + 22x / 8) = 8 * 78
56x + 22x = 624
78x = 624
Finally, divide both sides of the equation by 78 to solve for x:
x = 624 / 78
x = 8
Now that we have the value of x, we can find the volume of water in Container X:
Volume of water in Container X = 5x = 5 * 8 = 40 liters
b) To find the difference between the amount of water poured into Container X and Container Z, we need to compare their volumes:
Difference = Volume of water in Container X - Volume of water in Container Z
Difference = 5x - y
To find the value of y, we can substitute the value of x into either of the earlier equations. Let's use 7x + y = 78:
7 * 8 + y = 78
56 + y = 78
y = 78 - 56
y = 22
Difference = 5x - y = 5 * 8 - 22 = 40 - 22 = 18 liters
Therefore:
a) 40 liters of water was poured into Container X.
b) Container X had 18 liters more water poured into it than Container Z.
To solve this problem, we need to find the volume of water in each container one by one. Let's start with finding the volume of water in Container X.
Let X represent the volume of water in Container X.
Let Y represent the volume of water in Container Y.
Let Z represent the volume of water in Container Z.
We are given the ratio of the volume of water in Container X to Container Y as 5:2. This means that X/Y = 5/2.
Since we are told that Danny poured 78 liters of water into the three containers, we can set up an equation using this information:
X + Y + Z = 78
Now we can rearrange the first equation to solve for X in terms of Y:
X = (5/2)Y
Substituting this into the second equation, we get:
(5/2)Y + Y + Z = 78
Now let's find the ratio of the volume of water in Container Y to Container Z. We are given that it is 8:11, so Y/Z = 8/11.
We can substitute this into the equation above:
(5/2)Y + Y + (11/8)Y = 78
Now we can solve for Y:
(23/8)Y = 78
Y = (8/23) * 78
Y ≈ 33.91 liters
Now we can substitute the value of Y back into the equation for X:
X = (5/2) * 33.91
X ≈ 84.78 liters
So, a) Danny poured approximately 84.78 liters of water into Container X.
To find out how much more water was poured into Container X than Container Z, we need to subtract the volume of water in Container Z from the volume of water in Container X.
From the equations above, we don't have an explicit value for Z yet. However, we can use the equation X + Y + Z = 78 to solve for Z:
84.78 + 33.91 + Z = 78
Z = 78 - 84.78 - 33.91
Z = -40.69 liters
Since we can't have negative volume, we can conclude that there was an error in the calculations. Please double-check the given information and equations provided.