Let the cost of each bun in 8 count package is x and the cost of each bun in 10 count package is y.
It is given that the unit price of an 8-count package of hamburger buns is $ 0.03 more than the unit price of a 10-count package. So we can write the equation:
x = y + 0.03 (1)
The 8-count package costs $0.45 less than the cost of the 10-count package. We can write this in equation as:
8x = 10y - 0.45 (2)
Using the value of x from (1) in equation (2) we get:
8(y + 0.03) = 10y - 0.45
8y + 0.24 = 10y - 0.45
0.24 + 0.45 = 10y - 8y
0.69 = 2y
y = $ 0.345
This means the unit price of 10 count package of hamburger buns is $ 0.345. So the cost of entire pack will be 10 x 0.345 = $ 3.45
Thus, the cost of 10-count package is $3.45