數學問題(20分)

let y be the length of time that Noah travelled at 12km/h

18x+12y=69.....(1)
x+y=5...........(2)

from (2),x=5-y...(3)
sub (3) into (1)
18(5-y)+12y=69
-6y= -21
y= 3.5
(i) Noah travelled at 12km/h for 3.5 hours

(ii) Write an equation for x
18x+12*3.5 =69
(iii) Solve the equation obtained in (a)(ii). [show your working]

18x+12*3.5 =69
18x+42=69
18x=27
x=1.5

b)Is the solution obtained (a)(iii) the same as the solution of 6(x+5) = 48? Explain your answer.

no. "6(x+5) = 48" is not the correct equation for solving the time that used by Noah to travel at 18km/h

(a) (i) (5-x) hours
(ii) 18x + 12(5-x) = 69
(iii) 18x + 60 - 12x = 69
6x = 9
x=1.5
(b) solve 6(x+5)=48
(x+5) =8
x=3
Therefore, the solution obtained from (a)(iii) is different from above