how to solve word problem

Question

Last year you could get a hamburgedr, fries, and a cola at Francisco's for $2.70. Since the price of a hamburger has increased 20%, the price of fries has increased 10%, and the price of a cola has increased 50%, the same meal now costs $3.38. If the price of a cola in now 12 cents more than that of a hamburger, what was the price of each item last year?

Answer 1

Original price of hamburgers 90 cents

Original price of cola = 80 cents

Original price of fries = $1

90 + 100 + 80 = 270

New price of hamburgers = $1.08

New price of cola = $1.20

New price of fries = $1.10

H1= hamburger price last year

C1 = cola price last year

F1 = fries price last year

H2=hamburger price this year

C2 = cola price this year

F2 = fries price this year

H1 + F1 + C1 = 270

H2 + F2 + C2 = 338

C2= 1.5C1

H2 = 1.2H1

F2 = 1.1F1

C2 = 12 + H2

substitute values, subtract 338-270 = H2-H1 + F2-F1 + C2-C1

(5/6)H2 + (8/3)C2 = 410

H2 = (6/21)378 = 108

C2 = 120

H1 =H2/1.2 = 5/6(108) = 90 cents

C1 = C2/1.5 = 120/1.5 = 2/3(120) = 80 cents

F1 = F2/1.1 = 110/11 = $1