Question

For $1 you get 40 Cherries. For $3 you get 1 Orange. For $5 you get 1 Watermelon. Your mother told you to get 100 fruits for $100. How many of Cherries, Oranges and Watermelons will you buy?

Answer 1

80 cherries + 1 orange + 19 watermelon
.
To get 100 fruit you need to buy 80 cherries as you will not have enough money otherwise.
That leaves $98 for 20 fruit
1 orange = $3 => 3x = 1 fruit
1 watermelon = $5 => 5y = 1 fruit
3x + 5y = $98
x + y = 20 fruit => 3x + 3y = 60 => 3x = 60 - 3y
Combining the two
60 - 3y + 5y = 98 -> 2y = 38 => y = 19
19 watermelon + 1 orange