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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?

 Jul 10, 2024
 #1
avatar+1256 
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Let's write a system of equations to solve this problem.. 

Let's set b as bagel. 

Let's let m be muffin.

Let's let t be toast.

 

We have the system

\(2T + 1B = 3.15 \\ 1M + 1B = 3.50 \\ 1T + 2B + 3M = 8.15\)

 

We want to isolate b. From the first 2 equations, we can easily isolate the other two variables to only contain b, We have

\([3.15 - B ] / 2 = T \\ M = 3.50 - B\)

 

Now, we subsitute these two into the third equation. We get

\([ 3.15 - B ] / 2 + 2B + 3 [ 3.50 - B ] = 8.15 \\ [3.15 - B ] + 4B + 6 [ 3.50 -B ] = 16.30 \\ -3B + 3.15 + 21 = 16.30 \\ -3B = 16.30 - 3.15 - 21 \\ -3B = -7.85 \\ B = 7.85 / 3 ≈ $2.6.67\)

 

This is about 262 cents or 261 and 2/3 cents. 

 

Thanks! :)

 Jul 10, 2024

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