Question

Solve the following problems:

The total weight of three fruits boxes is $35\frac{1}{2}$ kg. If the box of grapes weighs $2$kg less than the box of apples and the box of apples weighs $1\frac{1}{2}$kg less than the box of oranges, find the weight of the three boxes.

Answer 1

Given, the total weight of three fruits boxes is $35\frac{1}{2}$ kg

Let the weight of the oranges box be $\mathrm{x}$ kg

So, Weight of the apple box is $\left(\mathrm{x}-1\frac{1}{2}\right)$ kg

Weight of grapes box is $\left[\left(\mathrm{x}-1\frac{1}{2}\right)-2\right]$ kg

According to the given condition,

Weight of the oranges box $+$ Weight of the apple box $+$Weight of grapes box $=35\frac{1}{2}$

$$\begin{gathered} \Rightarrow \mathrm{x}+\left(\mathrm{x}-1\frac{1}{2}\right)+\left[\left(\mathrm{x}-1\frac{1}{2}\right)-2\right]=35\frac{1}{2} \\ \Rightarrow \mathrm{x}+\left(\mathrm{x}-\frac{3}{2}\right)+\left[\left(\mathrm{x}-\frac{3}{2}\right)-2\right]=\frac{71}{2} \\ \Rightarrow \mathrm{x}+\mathrm{x}-\frac{3}{2}+\mathrm{x}-\frac{3}{2}-2=\frac{71}{2} \\ \Rightarrow 3\mathrm{x}-\frac{3}{2}-\frac{3}{2}-2=\frac{71}{2} \\ \Rightarrow 3\mathrm{x}-3-2=\frac{71}{2} \\ \Rightarrow 3\mathrm{x}-5=\frac{71}{2} \\ \Rightarrow 3\mathrm{x}-5+5=\frac{71}{2}+5[\mathrm{Adding}5\mathrm{to}\mathrm{both}\mathrm{sides}] \\ \Rightarrow 3\mathrm{x}=\frac{71+10}{2} \\ \Rightarrow 3\mathrm{x}=\frac{81}{2} \\ \Rightarrow \frac{3\mathrm{x}}{3}=\frac{81}{2\times 3} \\ \therefore \mathrm{x}=\frac{27}{2} \\ \mathrm{x}=13\frac{1}{2} \end{gathered}$$

So, the weight of the oranges box =$13\frac{1}{2}$kg

and Weight of the apple box = $\left(13\frac{1}{2}-1\frac{1}{2}\right)=\frac{27}{2}-\frac{3}{2}=\frac{24}{2}=12\mathrm{kg}$

The weight of the grapes box is $12-2=10\mathrm{kg}$

Hence, The weight of the apple box, grapes box, and oranges box is $12\mathrm{kg}$, $10\mathrm{kg}$ and $13\frac{1}{2}\mathrm{kg}$ respectively.