We appreciate your visit to The United States won 104 gold tex g tex silver tex s tex and bronze tex b tex medals in the 2012 Summer Olympics a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure, let's go through the solution step-by-step:
a. Linear Equation in Standard Form for Three Unknowns
We are told that the United States won a total of 104 gold, silver, and bronze medals in the 2012 Summer Olympics. This can be represented by the linear equation:
[tex]\[ g + s + b = 104 \][/tex]
where [tex]\( g \)[/tex] is the number of gold medals, [tex]\( s \)[/tex] is the number of silver medals, and [tex]\( b \)[/tex] is the number of bronze medals.
b. Relationship Between the Number of Silver and Bronze Medals
We are given in part (b) of the problem that the United States won 46 gold medals, and the same number of silver and bronze medals. This implies that the number of silver medals [tex]\( s \)[/tex] is equal to the number of bronze medals [tex]\( b \)[/tex]. Therefore, the relationship can be expressed as:
[tex]\[ s = b \][/tex]
c. Solving the Linear Equation
Given that there are 46 gold medals and [tex]\( s = b \)[/tex], we use this information to solve for the number of silver and bronze medals:
1. Substitute the gold medals into the equation from part (a): [tex]\( g = 46 \)[/tex].
2. The equation becomes [tex]\( 46 + s + b = 104 \)[/tex].
3. Since [tex]\( s = b \)[/tex], we can replace [tex]\( b \)[/tex] with [tex]\( s \)[/tex] in the equation:
[tex]\[ 46 + s + s = 104 \][/tex]
4. Simplify the equation:
[tex]\[ 46 + 2s = 104 \][/tex]
5. Solve for [tex]\( s \)[/tex]:
[tex]\[ 2s = 104 - 46 \][/tex]
[tex]\[ 2s = 58 \][/tex]
[tex]\[ s = 29 \][/tex]
6. Since [tex]\( s = b \)[/tex], we also have [tex]\( b = 29 \)[/tex].
So, the final medal count is:
- Gold medals, [tex]\( g = 46 \)[/tex]
- Silver medals, [tex]\( s = 29 \)[/tex]
- Bronze medals, [tex]\( b = 29 \)[/tex]
This gives us the complete solution for the number of each type of medal won by the United States.
a. Linear Equation in Standard Form for Three Unknowns
We are told that the United States won a total of 104 gold, silver, and bronze medals in the 2012 Summer Olympics. This can be represented by the linear equation:
[tex]\[ g + s + b = 104 \][/tex]
where [tex]\( g \)[/tex] is the number of gold medals, [tex]\( s \)[/tex] is the number of silver medals, and [tex]\( b \)[/tex] is the number of bronze medals.
b. Relationship Between the Number of Silver and Bronze Medals
We are given in part (b) of the problem that the United States won 46 gold medals, and the same number of silver and bronze medals. This implies that the number of silver medals [tex]\( s \)[/tex] is equal to the number of bronze medals [tex]\( b \)[/tex]. Therefore, the relationship can be expressed as:
[tex]\[ s = b \][/tex]
c. Solving the Linear Equation
Given that there are 46 gold medals and [tex]\( s = b \)[/tex], we use this information to solve for the number of silver and bronze medals:
1. Substitute the gold medals into the equation from part (a): [tex]\( g = 46 \)[/tex].
2. The equation becomes [tex]\( 46 + s + b = 104 \)[/tex].
3. Since [tex]\( s = b \)[/tex], we can replace [tex]\( b \)[/tex] with [tex]\( s \)[/tex] in the equation:
[tex]\[ 46 + s + s = 104 \][/tex]
4. Simplify the equation:
[tex]\[ 46 + 2s = 104 \][/tex]
5. Solve for [tex]\( s \)[/tex]:
[tex]\[ 2s = 104 - 46 \][/tex]
[tex]\[ 2s = 58 \][/tex]
[tex]\[ s = 29 \][/tex]
6. Since [tex]\( s = b \)[/tex], we also have [tex]\( b = 29 \)[/tex].
So, the final medal count is:
- Gold medals, [tex]\( g = 46 \)[/tex]
- Silver medals, [tex]\( s = 29 \)[/tex]
- Bronze medals, [tex]\( b = 29 \)[/tex]
This gives us the complete solution for the number of each type of medal won by the United States.
Thanks for taking the time to read The United States won 104 gold tex g tex silver tex s tex and bronze tex b tex medals in the 2012 Summer Olympics a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
