Milk mixture
In a container, milk and water are 7:5. If 15 L water is added, the ratio becomes 7:8. Find the quantity of water in the new mixture.
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Student
Initially, the ratio of milk to water is 7:5. This means that for every 7 parts of milk, there are 5 parts of water. Let's say the initial amount of milk is 7x and the initial amount of water is 5x.
Since 15 L of water is added, the new amount of water becomes 5x + 15.
The ratio of milk to water becomes 7:8, which means that for every 7 parts of milk, there are 8 parts of water (milk + water). We can set up an equation based on this:
(7x) / (5x + 15) = 7/8
To simplify this equation, we can cross-multiply:
7(5x + 15) = 8x
Expanding the left side, we get:
35x + 105 = 8x
Subtracting 8x from both sides gives us:
27x = -105
Dividing both sides by -27 gives us:
x = 105/27
So, the initial amount of water is 5x = 5(105/27) = 25 L.
The new amount of water is 5x + 15 = 25 + 15 = 40 L.
Therefore, the quantity of water in the new mixture is 40 L
Since 15 L of water is added, the new amount of water becomes 5x + 15.
The ratio of milk to water becomes 7:8, which means that for every 7 parts of milk, there are 8 parts of water (milk + water). We can set up an equation based on this:
(7x) / (5x + 15) = 7/8
To simplify this equation, we can cross-multiply:
7(5x + 15) = 8x
Expanding the left side, we get:
35x + 105 = 8x
Subtracting 8x from both sides gives us:
27x = -105
Dividing both sides by -27 gives us:
x = 105/27
So, the initial amount of water is 5x = 5(105/27) = 25 L.
The new amount of water is 5x + 15 = 25 + 15 = 40 L.
Therefore, the quantity of water in the new mixture is 40 L
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