Algebra - mixture problems

Question

Last year, Emma paid $19.70 for 3 kilograms of apples and 4 kilograms of cherries. This year, the price for apples increased by 20%, and the price for cherries increased by 30% due to bad weather conditions. This year she paid $28.30 for 2 kilograms of apples and 5 kilograms of cherries. What are this year's prices for one kilogram of apples and one kilogram of cherries?

Answer 1

1....3a+4c=19.70 or a=(19.70-4c)/3

2...2a*(1.2) +5c*(1.3)=28.30...2.4a =6.5c=28.3...a=(28.3 -6.5c)/2.4

(19.7-4c)/3=(28.3-6.5c)/2.4

or 2.4*(19.7-4c)=3(28.3-6.5c)

47.28-9.6c=84.9-19.5c

19.5c -9.6c=84.9-47.28

9.9c=37.62

c=3.8

a=(19.7-4c)/3=(19.7-15.2)/3....=4.5/3=1.5