for the equations y=5x+50 and y=6x+25, for how many hats will the cost be the same and what is that cost?
To find the number of hats for which the cost is the same and the corresponding cost, we need to solve the system of equations:
y = 5x + 50
y = 6x + 25
Setting the two expressions for y equal to each other, we get:
5x + 50 = 6x + 25
To solve for x, we can subtract 5x from both sides and subtract 25 from both sides:
50 - 25 = 6x - 5x
25 = x
So, the number of hats at which the cost is the same is x = 25.
To find the corresponding cost, substitute the value of x back into either equation:
y = 5x + 50
y = 5(25) + 50
y = 125 + 50
y = 175
Therefore, when x = 25, the cost (y) will be $175.