If 3 shirts and 4 caps cost $96, and 2 shirts and 5 caps cost $99, how much does each cap and each shirt cost?

x-cost\ of\ one\ shirt\\y-cost\ of\ one\ cap\\ \\3x+4y=\$96\ \ \ and\ \ \ 2x+5y=\$99\\ \\ \left \{ {{3x+4y=96\ /\cdot(-2)} \atop {2x+5y=99\ /\cdot(3)}} \right. \\ \\ \left \{ {{-6x-8y=-192} \atop {6x+15y=297} \right. \\ --------\\7y=105\ /:7\\\\y=15\ \ \Rightarrow\ \ 3x+4\cdot15=96\ \ \Rightarrow\ \ 3x=36\ /:3\ \ \Rightarrow\ \ x=12\\ \\Ans.\ one\ shirt\ cost\ \$12,\ \ one\ cap\ cost\ \$15

Answered by kate200468 | 2024-06-10

hmmm..... let us try again...but this time with a different strategy,.... by the graph method.
The system is
3x + 4y =96 2x + 5y = 99.
We find solutions of each system and then plot them on a graph.
Solutions for equation 1 = (2, 22.5) and (30, 0) Solutions for equation 2 = (49.5 , 0) and (1, 19.4)
Now, we plot both the equations on a graph paper and note its intersecting point.
Experimentally, we find the intersecting point is (12,15)
Thus, the solution for the system is x = 12 , y = 15.
Thus, we arrive at the conclusion 1 shirt costs 12 1 c a p cos t s 15

Answered by tadvisohil886 | 2024-06-10

The cost of one shirt is $12, and the cost of one cap is $15. This was determined by setting up and solving a system of equations based on the given information about the total costs. We eliminated variables to find the individual costs effectively.
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Answered by kate200468 | 2025-01-13