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At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does one bagel cost?

 Jun 3, 2023
 #1
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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. 

 

Thanks, James GBWA

 Jun 3, 2023
 #2
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Good work, Double-oh Seven, but with a simple mistake, I think.  

 

You lost me at    

 

                        Substituting the value of T back into Equation 4:

 

                        (80/3) - B = -235 

                        B = 235 - (80/3)      

 

Shouldn't this have been      B = 235 + (80/3) ???????  

       

From that we get                               705  +  80  

                                              B  =  ——–————  

                                                                3  

 

Which is                                 B  =  785 / 3  =  261.666667  

 

and that's the same answer that I got when I solved (tried to solve?)  

this problem at  https://web2.0calc.com/questions/system_86906  

 

I thought maybe there'd been something wrong, either with the problem  

or with my feeble efforts, since problems like this usually come out even.  

.

 Jun 3, 2023

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