Question

The weight of 26 packets of sugar is 55 kg 90 g. Find the weight of each packet.\[\]

Answer 1

Hint: We recall unitary method and direct variation because the given problem is in direct variation with quantities total weight of sugar say $a$ and number of packets say $b$. We first convert the total weight in kg by using metric conversion of weights as $1kg=1000g$. We use the unitary method and find the weight of one packet of sugar as $\dfrac{a}{b}$ .\[\]

Complete step by step answer:
We know that the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying with the single unit value. There are two types of two cases for unitary method one is direct variation and other is indirect variation. \[\]
When one quality $a$ increases with another quantity $b$ and also $a$ decreases with $b$ then we say the quantities $a$ and $b$ are in direct variation. Here the fraction $\dfrac{a}{b}$ always remains constant. We divide the increasing quantity $a$ by $b$ to obtain the value of a single unit and then multiply to find the required value. \[\]
We are given the question that the weight of 26 packets of sugar is 55 kg 90g. We know that 1kg=1000g. Let us convert the total weight into gram as
\[55kg\text{ 9g}=55\times 1000g+90g=55000g+90g=55090g\]
We know that $1g=\dfrac{1}{1000}\text{kg}$. We convert back the total weight into kg and in decimal as
\[55090\times \dfrac{1}{1000}=55.09\text{kg}\]
The total weight of the sugar increases with the number of packets. So the problem is in direct variation. Let us denote total weight of sugar as $a=55.09$ and the with number of packets as $b=26$.\[\]
The weight of 1 single packet is the value of a single unit here. So let us divide $a$ by $b$ and find the weight of 1 packet of sugar in kg as
\[\dfrac{a}{b}=\dfrac{55.09}{26}=2.1186\]
We round off up to two digits after the decimal point and have the weight of the packet as 2.12kg. \[\]

So, the weight of the packet is 2.12kg.

Note: We require the knowledge of decimal division and rounding off to solve this problem. We rounded up to two digits following the rule of significant figure that is the maximum number of digits that is meaningful to the question which is determined by here 55.09 as 4. We can also find the result in gram where we have to take 5 significant digits. We need to be careful of the confusion between direct and indirect variation where $a$ decreases with increase in $b$ and $ab$ remains constant.