The price of 4 citrons and 5 fragrant wood apples is 46 units. The price of 5 citrons and 4 fragrant wood apples is 53 units. Find the price of a citron and the price of a wood apple.

Answer 1

4 c + 5 a = 46
5 c + 4 a = 53

multiply first equation by 5 and second by 4
20 c + 25 a = 230
20 c + 16 a = 212
--------------------------- subtract
9 a = 18
a = 2 units per apple
then back to
4 c + 5 a = 46
4 c + 10 = 46
c = 36/4 = 9 units per lemon

Answer 2

4c + 5a = 46
5c + 4a = 53
Multiply first equation by 5 and second by 4.
20c + 25a = 230
20c + 16a = 212
Subtract second equation from first to solve for a. Insert that value into either of first two equations to solve for c.