Question

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

Answer 1

`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`

Answer 2

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 cap costs 15$