Question 845847
At McDonald's, four hamburgers and two orders of French fries cost $27.10.
 Three hamburgers and four orders of fries cost $25.20.
 If all hamburgers cost the same price and all orders of fries cost the same price, find the price of each. 
:
let h = price of the hamburger
let f = price of the fries
:
Write  two equations, one for each order
4h + 2f = 27.10
3h + 4f = 25.20
:
We will use elimination here; multiply the 1st equation by 2, subtract the 2nd equation
8h + 4f = 54.20
3h + 4f = 25.20
-------------------subtraction eliminates f, find h
5h = 29
h = 29/5
h = $5.80 for a hamburger
:
Find f using the 1st original equation, replace h with 5.80
4(5.8) + 2f = 27.10
23.20 + 2f = 27.10
2f = 27.10 - 23.20
2f = 3.90
f = 3.90/2
f = $1.95 for fries
:
:
Check solutions in the 2nd equation, replace h and f
3(5.80) + 4(1.95) = 
17.40 + 7.80 = 25.20, confirms our solutions