How much water should we add to 35 kg of sugar syrup to change its concentration from 30% to 25%?

35kg - a mass of sugar syrup

30% of 35kg it's a mass of sugar

30% = 30 : 100 = 0.3

30% of 35kg = 0.3 · 35kg = 10.5kg - a mass of sugar

Add xkg water. Then we have (35 + x)kg of sugar syrup and still 10.5kg of sugar.

10.5kg is 25% of (35 + x)kg .

(35 + x) -- 100%

10.5  -- 25%     multiply both sides by 4

42   -- 100%

Therefore we have the equation:

35 + x = 42      subtract 35 from both sides

x = 7