+253 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?
+1897 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! :)
