Let's assume the cost of one piece of toast is T cents, the cost of one bagel is B cents, and the cost of one muffin is M cents.

From the given information, we can create the following equations:

Equation 1: 2T + B = 315 (Mary's order)

Equation 2: B + M = 350 (Gary's order)

Equation 3: T + 2B + 3M = 815 (Larry's order)

To solve these equations, we can use a method called substitution.

From Equation 2, we can express M in terms of B: M = 350 - B

Now, let's substitute this value of M into Equation 3:

T + 2B + 3(350 - B) = 815

T + 2B + 1050 - 3B = 815

T - B = -235 ...(Equation 4)

We now have two equations with two variables: Equation 1 (2T + B = 315) and Equation 4 (T - B = -235).

Solving these equations simultaneously, we get:

2T + B = 315 ...(Equation 1)

T - B = -235 ...(Equation 4)

By adding Equation 1 and Equation 4 together, we eliminate B:

3T = 80

T = 80 / 3

Substituting the value of T back into Equation 4:

(80/3) - B = -235

B = 235 - (80/3)

Calculating the value of B:

B = 705/3

B = 235

Therefore, one bagel costs 235 cents.

I hope this answer help you to solve your question.