Question

A total of $1400kg$ of potatoes were sold in three days. On the first day, $100kg$ less potatoes were sold than on the second day, and on the third day, ${\left(\frac{3}{5}\right)}^{th}$ of the amount sold on the first day. How many kilograms of potatoes were sold on each day?

Answer 1

Find the weight of sold potatoes using linear equations.

Let the number of potatoes sold on the second day be $x$.

It is given that on the first day, $100kg$ less potatoes were sold than on the second day.

$\Rightarrow$The number of potatoes sold on the first day is $x-100$.

Also, it is given that on the third day, the number of potatoes sold were ${\left(\frac{3}{5}\right)}^{th}$ of the amount sold on the first day.

$\Rightarrow$The number of potatoes sold on the third day is $\frac{3}{5}\left(x-100\right)$.

We are given that a total of $1400kg$ of potatoes were sold in three days.

$\begin{array}{rcl}& \Rightarrow & x-100+x+\frac{3}{5}\left(x-100\right)=1400\\ & \Rightarrow & x-100+x+\frac{3}{5}x-60=1400\\ & \Rightarrow & \frac{13}{5}x-160=1400\\ & \Rightarrow & \frac{13}{5}x=1400+160\\ & \Rightarrow & \frac{13}{5}x=1560\\ & \Rightarrow & x=600\end{array}$

Hence, $600\text{kg}$ of potatoes were sold on the second day.

The number of potatoes sold on the first day is $x-100=600-100=500\text{kg}$.

The number of potatoes sold on the third day is $\frac{3}{5}\left(x-100\right)=\frac{3}{5}\left(600-100\right)=\frac{3}{5}\left(500\right)=300\text{kg}$.