7.1. There are 19 kg of cereal. Can 1 kg be measured with three weighings on a balance scale if there is one 3 kg weight?
Answer: It is possible. Solution. The first weighing can yield 8 kg of cereal. If a weight is placed on one (left) pan of the scales and, by pouring cereal from the right pan to the left, the scales are balanced. Indeed, from the equation $3+x=19-x$ we get $x=8$, i.e., there will be 8 kg of cereal on the pan with the weight. Leave 8 kg of cereal on the scales and, with the second weighing, divide this weight in half by pouring and balancing the pans of the scales. The last weighing will yield 1 kg if the weight is placed on one pan, and 4 kg of cereal on the other, and then 1 kg is poured (into a bag) to achieve balance.