Question

A van can carry a weight of 1250kg. How many cartons of fruits, each weighing 4kg 300g can be accommodated in the van?

Answer 1

Hint: The total weight that can be carried by the van is given to be 1250kg. The weight of each carton and the weight of each carton containing fruit is 4kg 300g. The total weight of the maximum numbers of cartons the van can carry must be less than or equal to 1250kg. We can determine the number of cartons that can be accommodated in the van by dividing the weight capacity of the van by the weight of one carton. For ease of calculation, we should convert the weight to the same unit, preferably grams.

Complete step by step solution:The maximum weight the van can carry
\[\begin{array}{l}
 = 1250{\rm{kg}}\\
 = 1250 \times 1000{\rm{g}}\\
 = 1.25 \times {10^6}{\rm{g}}
\end{array}\]
The weight of each carton containing fruits
\[\begin{array}{l}
 = 4{\rm{kg300g}}\\
 = 4 \times 1000 + 300{\rm{g}}\\
 = 4300{\rm{g}}\\
{\rm{ = 4}}{\rm{.3}} \times {\rm{1}}{{\rm{0}}^3}{\rm{g}}
\end{array}\]
The total weight of the maximum number of cartons that the van can carry \[ \le 1.25 \times {10^6}{\rm{g}}\].
Suppose that the maximum number of cartons the van can carry = n.
\[\begin{array}{l}
\therefore \left( {4.3 \times {{10}^3}} \right) \times n \le 1.25 \times {10^6}\\
 \Rightarrow n \le \dfrac{{1.25 \times {{10}^6}}}{{4.3 \times {{10}^3}}}\\
 \Rightarrow n \le \dfrac{{12500}}{{43}}\\
 \Rightarrow n \le 290.69
\end{array}\]
n must be a whole number less than 290.69.
n = 290
Maximum number of cartons that can be carried by the van = 290.

Note: To solve these kinds of questions, always convert all the weight to a common unit of measurement, gram or kg. Also remember that the number of cartons cannot be in fraction or decimals. It must be whole number less than the calculated value.