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Yoshiko used this linear system to represent a situation involving the costs of shirts and pants.

[tex]\[
\begin{array}{l}
3s + p = 130 \\
3s + 2p = 83
\end{array}
\][/tex]

What problem might Yoshiko have solved?

A. Three shirts and one pair of pants cost [tex]$130. Three shirts and two pairs of pants cost $[/tex]83. Determine the costs of one shirt and one pair of pants.

B. Three shirts and one pair of pants cost [tex]$130. Two shirts and three pairs of pants cost $[/tex]83. Determine the costs of one shirt and one pair of pants.

C. Three shirts cost [tex]$130. Three shirts and two pairs of pants cost $[/tex]83. Determine the costs of one shirt and one pair of pants.

D. Three shirts and four pairs of pants cost [tex]$130. Three shirts and two pairs of pants cost $[/tex]83. Determine the costs of one shirt and one pair of pants.

a. Problem D

b. Problem A

c. Problem B

d. Problem C

Sagot :

GinnyAnswer
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
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