SOLUTION: Entry fees for a race are $18 if registered before Oct.1 and $22 after. if a total of 1345 registered for the race and the entry fees totaled $25,766, how many people registered a

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Question 502317: Entry fees for a race are $18 if registered before Oct.1 and $22 after. if a total of 1345 registered for the race and the entry fees totaled $25,766, how many people registered after Oct. 1?
Answer by Maths68(1474) About Me  (Show Source):
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Let
Number of persons registered before 1 October = x
Number of persons registered after 1 October = y
Registration fee for before 1 October = 18
Registration fee for After 1 October = 22
Total registration fee before 1 October = x * 18=18x
Total registration fee after 1 October = y * 22=22y
Given
Sum of registered persons after and before the 1 October = Total registered persons
x+y=1345
x=1345-y .................(1)
Total registration fee before 1 October + Total registration fee after 1 October = Total registration fee
18x+22y=25766.............(2)
Put the value of x from (1) to (2)
18x+22y=25766
18(1345-y)+22y=25766
24210-18y+22y=25766
24210+4y=25766
4y=25766-24210
4y=1556
Divide by 4 both sides of the above equation
4y/4=1556/4
y=389
Number of persons register after 1 October = 389
Number of persons register before 1 October = 1345-389 = 956