Answer:
Let's start by assigning variables to the unknowns in the problem:
Let x be the selling price of a cup of apple juice.
Then the selling price of a cup of lemon juice is 3/2 times x, or 1.5x.
Let y be the number of times 2 cups of lemon juice are sold (so y is an even number).
Then the number of times 5 cups of apple juice are sold is 5/2 times y, or 2.5y.
From the given information, we can set up two equations:
2.5y(x + 12) = 1.5xy (Mr Tan earns $12 more from apple juice than from lemon juice)
2(1.5x)y = 5(2.5y) (for every 2 cups of lemon juice sold, 5 cups of apple juice are sold)
Simplifying the second equation, we get:
3xy = 25y
Dividing both sides by y (which is non-zero since y is even), we get:
3x = 25
Solving for x, we get:
x = 25/3
Substituting x into the first equation and simplifying, we get:
y = 24
So Mr Tan sells 24 cups of lemon juice and 60 cups of apple juice. To find his total earnings, we can multiply the selling price by the number of cups sold for each juice and add them up:
Total earnings = 24(1.5x) + 60x
Total earnings = 36x + 60x
Total earnings = 96x
Substituting x = 25/3, we get:
Total earnings = 96(25/3)
Total earnings = 800
Therefore, Mr Tan earns $800 altogether.