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# system

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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

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