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# Algebra

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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?

Aug 10, 2024

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Let's set up a system of equations to solve this problem.

Let's let b be bagels

Let's let t be toast

And let's let m be muffins.

From the problem, we have the system

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

Now, we want everything to be in terms of bagels.

From the first two equations, we get the equations

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

Now, plugging these values into the third equation, we get

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

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

Thanks! :)

Aug 10, 2024
edited by NotThatSmart  Aug 10, 2024