A can of milk is 3/4 full. When 30 litres of milk sold, the can still had 2/5 th full. Find the capacity of the can
3/4 x - 30 = 2/5 x
Now just solve for x
Well, it sounds like that can of milk is quite the optimist! Selling 30 liters of milk and still having 2/5ths of the can full? That's impressive. Based on that information, we can assume that 2/5ths of the can is equal to 30 liters.
Let's do some calculations! If 2/5 equals 30 liters, then 1/5th of the can must be 15 liters. Therefore, the capacity of the can is 5/5, which is the whole can, equal to 75 liters.
So, the can has a capacity of 75 liters. It must have some magic powers to still be partially full after selling 30 liters. Maybe it's secretly a clown car in disguise!
Let's solve this step by step:
Step 1: Let's assume the capacity of the can is C liters.
Step 2: According to the given information, the can is initially 3/4 full, which means there is ((3/4) * C) liters of milk in the can.
Step 3: After selling 30 liters of milk, the can is still 2/5 full, which means ((2/5) * C) liters of milk remains in the can.
Step 4: Since the amount of milk remaining in the can after selling 30 liters is ((2/5) * C), and we initially had ((3/4) * C) liters of milk in the can, we can set up the following equation:
((2/5) * C) = ((3/4) * C) - 30
Step 5: Let's solve for C by multiplying both sides of the equation by the least common denominator (20) to get rid of the fractions:
20 * ((2/5) * C) = 20 * ((3/4) * C) - 20 * 30
Step 6: Simplifying the equation, we have:
8C = 15C - 600
Step 7: Moving all the C terms to one side and the constant terms to the other side of the equation, we get:
8C - 15C = -600
Step 8: Simplifying the equation further, we have:
-7C = -600
Step 9: To solve for C, we divide both sides of the equation by -7:
C = (-600) / (-7)
Step 10: Dividing -600 by -7 we get:
C = 85.71 (rounded to two decimal places)
So, the capacity of the can is approximately 85.71 liters.
To find the capacity of the can, we need to determine the amount of milk that was originally in it.
Let's start by calculating the amount of milk remaining in the can after 30 liters were sold. We know that when the can had 30 liters less milk, it was still 2/5 full.
If we represent the original amount of milk as "x" liters, then (2/5)x liters remained after 30 liters were sold.
This can be expressed as an equation: (3/4)x - 30 = (2/5)x.
To solve this equation, we can eliminate the fractions by multiplying both sides by the least common denominator of 20, which is the product of the denominators 4 and 5:
20 * (3/4)x - 20 * 30 = 20 * (2/5)x.
Simplifying this equation gives us:
15x - 600 = 8x.
Next, we can isolate the "x" term by subtracting 8x from both sides:
15x - 8x - 600 = 0.
Combining like terms:
7x - 600 = 0.
Finally, we can solve for x by bringing the constant term to the other side:
7x = 600.
Dividing both sides by 7:
x = 600 / 7.
So, the original amount of milk in the can (the capacity of the can) is approximately 85.71 liters.