The Two Mangoes Problem

Solution:  

(1)  If one mango and one banana cost $4.70, then two bananas and two mangoes cost twice as much:  $9.40.
(2)  From there we can use the middle bag to find the cost of a single banana:  $13.00 (2 mangoes and 5 bananas) - $9.40 (2 mangoes and 2 bananas) = $3.60 (3 bananas).   If 3 bananas cost $3.60, then each banana costs $1.20.
(3)  From the first bag then we can see that a single mango costs $3.50 ($4.70-$1.20), and so the bag of 2 mangoes costs $7.00.