+1839 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?
+129881 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
