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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?

 Apr 9, 2024
 #1
avatar+128794 
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2T + 1B =  3.15     →  2T   = 3.15   - 1B    →   [3.15 - B ]  / 2  =  T         (1)

1M + 1B  = 3.50  →   M = 3.50 - B          (2)

1T + 2B + 3M  = 8.15     (3)

 

Sub (1) and (2)  into (3)

 

[ 3.15 - B ] / 2  +  2B  + 3 [ 3.50 - B ]  = 8.15               mutiply through by 2

 

[3.15 -  B ] + 4B  + 6 [ 3.50 -B ] = 16.30

 

-3B + 3.15 + 21  = 16.30

 

-3B  =  16.30 - 3.15 - 21

 

-3B = -7.85

 

B =  7.85 / 3  ≈  $2.62 = 262 cents

 

cool cool cool

 Apr 9, 2024

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