If 3 apples and 4 bananas cost 1.37 total and 5 apples and 7 bananas cost 2.36 total what is the total cost of 1 Apple and 1 banana?

Let $x and $y be the cost of an apple and a banana respectively

3x+4y=1.37 ... (1)

5x+7y=2.36 ... (2)

(1) * 5, 15x+20y=6.85 ... (3)

(2) * 3, 15x+21y=7.08 ... (4)

(4) - (3), y=0.23

sub. y=0.23 into (1), 3x+4*0.23=1.37

x=0.15

total cost=0.15+0.23=0.38