Respuesta :
the total weight of 6 pieces of butter and bag of sugar is 3.8 lb
lets name a piece of butter as x
there are 6 pieces of butter - then x * 6 = 6x
if we write an equation for the total cost
6x + bag of sugar = 3.8 lb
weight of bag of sugar = 1.4 lb
6x + 1.4 lb = 3.8 lb
6x = 3.8 - 1.4
6x = 2.4 lb
x = 2.4/6
x = 0.4 lbs
therefore weight of a piece of butter is 0.4 lbs
The weight of each piece of butter is [tex]\boxed{\bf0.4{\text{ lbs}}}[/tex].
Further explanation:
Given:
The total weight of 6 pieces of butter and the weight of a bag of sugar is equal to 3.8 lbs.
The weight of the bag of sugar is 1.4 lbs.
Our aim is to find the weight of each piece of butter.
Calculation:
Let the weight of each piece of butter to be [tex]x[/tex] lbs.
Also consider the weight of a bag of sugar to be [tex]y[/tex] lbs.
Then the weight of 6 pieces of butter is [tex]\boxed{6x}[/tex].
Therefore, the total weight of 6 pieces of butter and one bag of sugar is calculated as.
[tex]{\text{Total weight}}=6x+y[/tex]
Given that total weight of 6 pieces of butter and one bag of sugar is equal to 3.8.
Now, the total weight in the form of an equation can be written as,
[tex]6x+y=3.8[/tex] ……(1)
Since, the weight of one bag of sugar is equal to 1.4 lbs., then substitute 1.4 for [tex]y[/tex] in equation (1) to obtain the value of [tex]x[/tex] as follows:
[tex]6x+1.4=3.8[/tex]
Subtract 1.4 on both sides of above equation as follows:
[tex]\begin{aligned}6x+1.4-1.4&=3.8-1.4\\6x&=2.4\\\end{aligned}[/tex]
Now, divide both sides of above equation by 6 to obtain the value of [tex]x[/tex] as follows:
[tex]\begin{aligned}\frac{{6x}}{6}&=\frac{{2.4}}{6}\\x&=0.4\\\end{aligned}[/tex]
Therefore, the weight of each piece of butter is equal to [tex]\boxed{\bf0.4{\text{ lbs}}}[/tex].
Learn more:
1. Learn more about equations https://brainly.com/question/788903
2. Learn more about algebraic expression https://brainly.com/question/5533462
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Linear equations
Keywords: Weight, pieces, butter, bag, sugar, total, lbs., equations, algebraic equations, linear, subtract, 6x+y=3.8, x=0.4.
