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?

magenta Sep 25, 2024

#1**+1 **

From the problem, we can write the system

where t is toast, b is bagel and m is muffin.

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

From the first two equations, we have

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

Subbing this in to the third equation, we have

\([ 3.15 - B ] / 2 + 2B + 3 [ 3.50 - B ] = 8.15 \\ [3.15 - B ] + 4B + 6 [ 3.50 -B ] = 16.30 \\ -3B + 3.15 + 21 = 16.30 \\ -3B = 16.30 - 3.15 - 21 \\ -3B = -7.85 \\ B = 7.85 / 3 ≈ $2.62\)

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

Thanks! :)

NotThatSmart Sep 25, 2024