Two types of boxes A, B are to be placed in a truck having capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still ...

Answer: Box A weighs 30 kg and box B weighs 55 kg

1 ton = 1000 kg, so 10 tons = 10000 kg. Let one box of type A weigh \(x\) kg and one box of type B weigh \(y\) kg.

\(150x + 100y = 10000\), i.e. \(3x + 2y = 200\) ... (I)
\(260x + 40y = 10000\), i.e. \(13x + 2y = 500\) ... (II)

Subtract (I) from (II): \(10x = 300\), so \(x = 30\).

From (I): \(2y = 200 - 90 = 110\), so \(y = 55\).

Check: \(150(30) + 100(55) = 4500 + 5500 = 10000\) kg, which is true.