Answer :
To determine which problem Yoshiko might have solved, let's examine each of the given choices and see if they accurately describe the system of linear equations:
[tex]\[ \begin{array}{l} 3s + p = 130 \\ 3s + 2p = 83 \end{array} \][/tex]
Choice A:
Three shirts and one pair of pants cost \[tex]$130. Three shirts and two pairs of pants cost \$[/tex]83.
1. Three shirts and one pair of pants cost \[tex]$130: This matches the equation \(3s + p = 130\). 2. Three shirts and two pairs of pants cost \$[/tex]83: This matches the equation [tex]\(3s + 2p = 83\)[/tex].
So, Choice A correctly matches the system of equations.
Choice B:
Three shirts and one pair of pants cost \[tex]$130. Two shirts and three pairs of pants cost \$[/tex]83.
1. Three shirts and one pair of pants cost \[tex]$130: This matches the equation \(3s + p = 130\). 2. Two shirts and three pairs of pants cost \$[/tex]83: However, this would be translated to [tex]\(2s + 3p = 83\)[/tex], which does not match [tex]\(3s + 2p = 83\)[/tex].
So, Choice B does not correctly match the system of equations.
Choice C:
Three shirts cost \[tex]$130. Three shirts and two pairs of pants cost \$[/tex]83.
1. Three shirts cost \[tex]$130: This matches the equation \(3s = 130\), which is different from \(3s + p = 130\). 2. Three shirts and two pairs of pants cost \$[/tex]83: This matches the equation [tex]\(3s + 2p = 83\)[/tex].
So, Choice C does not correctly match the system of equations.
Choice D:
Three shirts and four pairs of pants cost \[tex]$130. Three shirts and two pairs of pants cost \$[/tex]83.
1. Three shirts and four pairs of pants cost \[tex]$130: This matches the equation \(3s + 4p = 130\), which is different from \(3s + p = 130\). 2. Three shirts and two pairs of pants cost \$[/tex]83: This matches the equation [tex]\(3s + 2p = 83\)[/tex].
So, Choice D does not correctly match the system of equations.
Based on this analysis, the best match to the given system of equations is Choice A.
Hence, the correct answer is:
b. Problem A
[tex]\[ \begin{array}{l} 3s + p = 130 \\ 3s + 2p = 83 \end{array} \][/tex]
Choice A:
Three shirts and one pair of pants cost \[tex]$130. Three shirts and two pairs of pants cost \$[/tex]83.
1. Three shirts and one pair of pants cost \[tex]$130: This matches the equation \(3s + p = 130\). 2. Three shirts and two pairs of pants cost \$[/tex]83: This matches the equation [tex]\(3s + 2p = 83\)[/tex].
So, Choice A correctly matches the system of equations.
Choice B:
Three shirts and one pair of pants cost \[tex]$130. Two shirts and three pairs of pants cost \$[/tex]83.
1. Three shirts and one pair of pants cost \[tex]$130: This matches the equation \(3s + p = 130\). 2. Two shirts and three pairs of pants cost \$[/tex]83: However, this would be translated to [tex]\(2s + 3p = 83\)[/tex], which does not match [tex]\(3s + 2p = 83\)[/tex].
So, Choice B does not correctly match the system of equations.
Choice C:
Three shirts cost \[tex]$130. Three shirts and two pairs of pants cost \$[/tex]83.
1. Three shirts cost \[tex]$130: This matches the equation \(3s = 130\), which is different from \(3s + p = 130\). 2. Three shirts and two pairs of pants cost \$[/tex]83: This matches the equation [tex]\(3s + 2p = 83\)[/tex].
So, Choice C does not correctly match the system of equations.
Choice D:
Three shirts and four pairs of pants cost \[tex]$130. Three shirts and two pairs of pants cost \$[/tex]83.
1. Three shirts and four pairs of pants cost \[tex]$130: This matches the equation \(3s + 4p = 130\), which is different from \(3s + p = 130\). 2. Three shirts and two pairs of pants cost \$[/tex]83: This matches the equation [tex]\(3s + 2p = 83\)[/tex].
So, Choice D does not correctly match the system of equations.
Based on this analysis, the best match to the given system of equations is Choice A.
Hence, the correct answer is:
b. Problem A
