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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 two muffins, which comes out to $4.85. Larry orders a piece of toast, two bagels, and a muffin, which comes out to $5.25. How many cents does one bagel cost?

 Jul 10, 2024
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We put the system in matrix form:

 

[2 1 0] [t] = 3.15

[0 2 1] [b] = 4.85

[1 2 1] [m] = 5.25

 

Solving, we get b = 1.40, t = 1.20, m = 1.60.  Therefore, one bagel costs 140 cents.

 Jul 10, 2024

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