Solution:
This problem is a system of linear equations in two variables problem. Representing the cost of each fruit
Let x be the cost of bananas
y be the cost of mangoes
Converting word problem to mathematical equation
5x + 3y = 90 Eq. 1
3x + 5y = 118 Eq. 2
Multiplying Eq. 1 by 5
(5x + 3y = 90) × 5
25x + 15y = 450 Eq. 3
Multiplying Eq. 2 by -3
(3x + 5y = 118) × -3
-9x - 15y = -354 Eq. 4
Adding Eq. 3 and Eq. 4
25x + 15y = 450
+ -9x - 15y = -354
16x = 96
Solving for x
x = 6
Solving for y (using Eq. 1)
5(6) + 3y = 90
30 + 3y = 90
3y = 90 - 30
3y = 60
y = 20
Therefore, the cost of bananas is Php 6 and the cost of mangoes is Php 20.
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