Certainly! Let's solve this step-by-step:
1. Understanding the Problem:
We need to find the cost of one pair of trousers and the cost of four shirts given the following information:
- The total cost of three pairs of trousers and two shirts is [tex]$2400.
- The total cost of two pairs of trousers and three shirts is $[/tex]1975.
2. Formulating the Equations:
Let [tex]\( T \)[/tex] be the cost of one pair of trousers, and [tex]\( S \)[/tex] be the cost of one shirt.
According to the given information, we can write the following system of linear equations:
- [tex]\( 3T + 2S = 2400 \)[/tex] ...(Equation 1)
- [tex]\( 2T + 3S = 1975 \)[/tex] ...(Equation 2)
3. Solving the System of Equations:
By solving these two linear equations simultaneously, we can find the values of [tex]\( T \)[/tex] and [tex]\( S \)[/tex]:
- [tex]\( T = 650 \)[/tex]
- [tex]\( S = 225 \)[/tex]
4. Finding the Required Costs:
- The cost of one pair of trousers ([tex]\( T \)[/tex]) is [tex]\( 650 \)[/tex].
- To find the cost of four shirts ([tex]\( 4S \)[/tex]), we multiply the cost of one shirt by 4:
[tex]\( 4S = 4 \times 225 = 900 \)[/tex].
5. Conclusion:
- The cost of one pair of trousers is [tex]$650.
- The cost of four shirts is $[/tex]900.
