At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and two muffins, which comes out to $4.85. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.25. How many cents does one bagel cost?

Answer 1

Let t be the cost of one piece of toast, b be the cost of one bagel, and m be the cost of one muffin. We can set up the following system of equations:

2t + b = 315 (Mary's order)
b + 2m = 485 (Gary's order)
t + 2b + 3m = 825 (Larry's order)

We want to find the value of b.

From the first equation, we can solve for t:

2t + b = 315
2t = 315 - b
t = (315 - b)/2

Substituting this into the third equation:

(315 - b)/2 + 2b + 3m = 825

Multiplying both sides by 2 to get rid of the fraction:

315 - b + 4b + 6m = 1650

Simplifying:

3b + 6m = 1335

Dividing by 3:

b + 2m = 445

Now we have two equations in two variables:

2t + b = 315
b + 2m = 445

Solving for b in the second equation:

b = 445 - 2m

Substituting this into the first equation:

2t + (445 - 2m) = 315

Simplifying:

2t - 2m = -130

Dividing by 2:

t - m = -65

Now we can solve for m in terms of t:

m = t + 65

Substituting back into the second equation:

b + 2(t + 65) = 445

Solving for b:

b + 2t + 130 = 445

b = 315 - 2t

Substituting into the first equation:

2t + (315 - 2t) = 315

2t = 0

t = 0

Substituting t = 0 back into the equation for b:

b = 315 - 2t = 315

Therefore, one bagel costs 315 cents.