A tank is 5/7 full, when 440 litres are removed it goes to 2/5. How much litres does it contain in full capacity
full capacity ---- x litres
(5/7)x - 440 = (2/5)x
multiply by 35 , the LCD
25x - 15400 = 14x
take over
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To find out the full capacity of the tank, we need to determine how much liquid is represented by the difference between 2/5 and 5/7 of the tank's capacity.
Let's break down the problem step by step:
1. Start by assigning variables:
- Let x represent the full capacity of the tank in liters
2. First, determine the amount of liquid represented by 5/7 of the tank's capacity:
- (5/7) * x
3. Next, determine the amount of liquid represented by 2/5 of the tank's capacity:
- (2/5) * x
4. We are told that when 440 liters are removed from the tank, it goes from being 5/7 full to 2/5 full. We can express this as an equation:
- (5/7) * x - 440 = (2/5) * x
5. Now, solve the equation for x to find the full capacity of the tank:
- Multiply both sides of the equation by the least common denominator (LCD) of 7 and 5, which is 35. This will eliminate the denominators.
- 35 * ((5/7) * x - 440) = 35 * ((2/5) * x)
- 5 * 5 * x - 35 * 440 = 7 * 2 * x
- 25x - 15400 = 14x
6. Simplify the equation and solve for x:
- Subtract 14x from both sides:
- 25x - 14x - 15400 = 0
- 11x - 15400 = 0
- Add 15400 to both sides:
- 11x = 15400
- Divide both sides by 11:
- x = 1400
Therefore, the full capacity of the tank is 1400 liters.