Let's define
b: cost of a bagel
m: cost of a muffin
8 bagels and 6 muffins cost $13.80 means:
8b + 6m = 13.80 (eq. 1)
4 bagels and 12 muffins cost $18.60 means:
4b + 12m = 18.6 (eq. 2)
Multiplying equation 2 by 2, we get:
2(4b + 12m) = 2(18.6)
2(4b) + 2(12m) = 2(18.6)
8b + 24m = 37.2 (eq.3)
Subtracting equation 1 to equation 3:
8b + 24m = 37.2
-
8b + 6m = 13.80
------------------------------
18m = 23.4
m = 23.4/18
m = 1.3
Replacing m = 1.3 into equation 1:
8b + 6(1.3) = 13.80
8b + 7.8 = 13.80
8b = 13.8 - 7.8
8b = 6
b = 6/8
b = 0.75
Bagels cost $0.75 and muffins cost $1.3