2/5 of a pool was filled with water. after pouring out 5/7 of the amount of water in the pool, 62 liters of water was needed to fill the pool completely. Find the amount of water needed to fill up the empty pool

2/5 x - (5/7)(2/5 x) + 62 = x

x = 70

To find the amount of water needed to fill up the empty pool, we will first calculate the current amount of water in the pool.

Let's assign a variable to the total capacity of the pool, which we'll call "C." Since 2/5 of the pool was filled, the amount of water in the pool is 2/5 of C.

Therefore, the current amount of water in the pool is (2/5)C.

Next, we pour out 5/7 of the amount of water in the pool. This means we remove (5/7) * (2/5)C = (10/35)C = (2/7)C of water from the pool.

After pouring out this amount, we need 62 liters of water to fill the pool completely. So, this remaining amount is equal to 62 liters.

Hence, we can write the equation:

(2/7)C - 62 = 0

To solve for C, let's isolate the variable. We'll first add 62 to both sides of the equation:

(2/7)C = 62

Then, we can multiply both sides of the equation by the reciprocal of (2/7), which is (7/2):

C = 62 * (7/2)

C = 217

Therefore, the total capacity of the empty pool is 217 liters.