To solve the given problem, let's define the variables first. Let [tex]\( J \)[/tex] be the cost of the jacket and [tex]\( s \)[/tex] be the cost of the slacks. According to the problem, we have two pieces of information:
1. The total cost of the jacket and the slacks is \[tex]$63.
2. The jacket costs \$[/tex]33 more than the slacks.
These pieces of information can be translated into the following system of equations:
[tex]\[ J + s = 63 \][/tex]
[tex]\[ J - s = 33 \][/tex]
To solve this system of equations, we can use the method of addition (also known as the elimination method). By adding both equations together, we can eliminate one of the variables. Here’s how it works:
[tex]\[ J + s = 63 \][/tex]
[tex]\[ J - s = 33 \][/tex]
Adding these equations together:
[tex]\[ (J + s) + (J - s) = 63 + 33 \][/tex]
[tex]\[ 2J = 96 \][/tex]
Now, divide both sides by 2 to solve for [tex]\( J \)[/tex]:
[tex]\[ J = \frac{96}{2} \][/tex]
[tex]\[ J = 48 \][/tex]
So, the jacket costs \[tex]$48.
Now, to determine the cost of the slacks \( s \), we can substitute \( J = 48 \) back into one of the original equations. Let's use the first equation:
\[ 48 + s = 63 \]
Subtract 48 from both sides to solve for \( s \):
\[ s = 63 - 48 \]
\[ s = 15 \]
So, the slacks cost \$[/tex]15.
Therefore, Mr. Rose paid \[tex]$48 for the jacket and \$[/tex]15 for the slacks.
The correct system of equations that represents the word problem is:
[tex]\[ J + s = 63 \][/tex]
[tex]\[ J - s = 33 \][/tex]
