In a certain clothing store, 3 shirts and 5 ties cost $60, and 2 shirts and 3 ties cost $39. What is the cost of each shirt?
Let's call the cost of one shirt "s" and the cost of one tie "t". Then we can set up two equations based on the information given:
3s + 5t = 60
2s + 3t = 39
We can use these equations to solve for s. One way to do this is to solve one of the equations for one variable (in terms of the other variable), and then substitute that expression into the other equation. For example, we could solve the second equation for t:
2s + 3t = 39
3t = 39 - 2s
t = (39 - 2s)/3
Now we can substitute this expression for t into the first equation:
3s + 5t = 60
3s + 5((39 - 2s)/3) = 60
This gives us an equation with only one variable, which we can solve:
3s + (195 - 10s)/3 = 60
9s + 195 - 10s = 180
-s + 195 = 180
-s = -15
s = 15
So the cost of one shirt is $15. We can check this by plugging s = 15 into one of the original equations and solving for t:
3s + 5t = 60
3(15) + 5t = 60
45 + 5t = 60
5t = 15
t = 3
Therefore, the cost of one tie is $3.