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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 four muffins, which comes out to 7.85.  Larry orders a piece of toast, two bagels, and three muffins, which comes out to 9.75.  How many cents does one bagel cost?

 Oct 28, 2023
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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 four muffins, which comes out to 7.85.  Larry orders a piece of toast, two bagels, and three muffins, which comes out to 9.75.  How many cents does one bagel cost?  

 

wiseowl, what's up with the about a million postings?  Is this your homework or what?  

 

T is for toast  

B is for bagel  

M is for muffin  

 

                                         2T + B  =  315    (I'm using cents because the answer will be in cents.)  

                                         B + 4M  =  785  

                                         T + 2B + 3M  =  975  

 

from 1st equation              2T = (315 – B)   so   T = (315 – B) / 2   

from 2nd equation             4M = (785 – B)   so   M = (785 – B) / 4  

 

Now we have T and M in terms of B so substitute it into the 3rd equation.  

 

                                          (315 – B)           2B          3 • (785 – B)  

                                          ––––––––   +   ––––   +   ––––––––––  =  975  

                                                 2                  1                    4  

 

Let's get rid of those denominators by multiplying both sides times 4.  

 

                                           2 • (315 – B)  +  4 • 2B  +  1 • 3 • (785 – B)  =  4 • 975   

 

Multiply it out                       (630 – 2B)  +  8B  +  (2355 – 3B)  =  3900  

 

Combine like terms              3B  =  915  

 

                                              B  =  305  ......  One bagel costs 305 ¢  

 

Plugging into original equations, a toast costs 5¢ and a muffin costs 120¢ 

.

 Oct 28, 2023

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