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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?

 May 30, 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 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?  

 

Looks like a substitution problem.  Let's see what we've got.  

 

Mary's order:                                   2T + B  =  3.15  

Gary's order:                                   B + M  =  3.50  

Larry's order:                                   T + 2B + 3M  =  8.15  

 

per Mary's                                         2T + B  =  3.15  

                                                                2T  =  3.15 – B  

                                                                   T  =  (3.15 – B) / 2  

 

per Gary's                                            B + M  =  3.50  

                                                                   M  =  3.50 – B  

 

Now we have the toast and the  

muffin in terms of the bagel, so  

substitute into Larry's order                 T + 2B + 3M  =  8.15  

 

                                                            [(3.15 – B) / 2]  +  2B  +  (3)(3.50 – B)  =  8.15  

 

Multiply everything by 2, to get  

rid of that denominator                               (3.15 – B)  +  4B  +  (6)(3.50 – B)  =  16.30  

 

Now it's just a question of

multiplying and adding; it's  

tedious, but simple.                              3.15 – B + 4B + 21.00 – 6B  =  16.30  

                                                                                      24.15 – 3B  =  16.30  

                                                                                                – 3B  =  16.30 – 24.15  

                                                                                                – 3B  =  – 7.85  

 

Usually, the problems like this are                                                B  =  2.61667 dollars     

crafted to come out even.  I have  

gone over this thing, I don't know,                                                B  =  262 ¢  

probably 20 times and I can not  

find a mistake.  I would gratefully  

appreciate it, if some one spots  

a mistake, post a comment telling  

me where I messed up.  Thanks.  

.

 May 30, 2023

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