Question

the total weight of 6 pieces of butter and a bag of sugar is 3.8 Ib. if the weight of the bag of sugar is 1.4 Ib, what is the weight of each piece of butter?

Answer 1

0.4 lbs each.

Further explanation

Given:

• The total weight of 6 pieces of butter and a bag of sugar is 3.8 Ib.
• The weight of the bag of sugar is 1.4 Ib

Question:

What is the weight of each piece of butter?

The Process:

The two steps for obtaining the weight of each piece of butter are as follows:

Step-1: the total amount of butter is the total bag of butter and sugar subtracted by the weight of the bag of sugar.

$\boxed{ \ 3.8 \ lbs - 1.4 \ lbs = 2.4 \ lbs \ }$

Step-2: the total amount of butter divided by the number of pieces of butter is the the weight of each piece of butter.

$\boxed{ \ 2.4 \ lbs \div 6 \ pieces = \boxed{ \ 0.4 \ lbs/piece \ } \ }$

Let's also consider the following quick steps.

Quick steps:

$\boxed{ \ \frac{(3.8 - 1.4) \ lbs}{6 \ pieces} = \boxed{ \ 0.4 \ lbs/piece \ } \ }$

Therefore, the weight of each piece of butter is 0.4 lbs.

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Keyword: the total weight, 6 pieces of butter, a bag of sugar is 3.8 Ib, if the weight of the bag of sugar is 1.4 Ib, each piece, subtracted, divide

Answer 2

The weight of each piece of butter is $\boxed{\bf 0.4\text{ lb}}$.

Further explanation:

The total weight of $6$ pieces of butter and the weight of a bag of sugar is equal to $\bf 3.8\text{ lb}$.

It is given that the weight of the bag of sugar is $1.4\text{ lb}$.

Now, let the weight of each piece of butter to be $x\text{ lb}$.

Then the weight of $6$ pieces of butter is $6x$.

Therefore, the total weight of $6$ pieces of butter and one bag of sugar is calculated as,

$\text{Total weight}=6x+1.4$

Given that total weight of $6$ pieces of butter and one bag of sugar is equal to $3.8 \text{ lb}$.

Then, the total weight in the form of an equation can be written as,

$\boxed {6x+1.4=3.8}$

Subtract $1.4$ on both sides of the above equation as follows:

$\begin{aligned} 6x+1.4-1.4&=3.8-1.4\\6x&=2.4 \end{aligned}$

Now, divide both sides of above equation by $6$ to obtain the value of $x$ as follows:

$\begin{aligned} \dfrac{6x}{6} &=\dfrac{2.4}{6} \\x&=0.4 \end{aligned}$

Thus, the weight of each piece of butter is $\boxed{\bf 0.4\text{ lb}}$.

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Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Linear equations

Keywords: Weight, pieces, butter, bag, sugar, total, lbs, equations, algebraic equations, linear, subtract, $6x+1.4=3.8$, $x=0.4$, divide, total weight, each piece of butter.