1. The unit digit of a two-digit number is twice that of its tens digit. If the tens digit and the units digit are interchanged, then the new number is smaller than twice the original number by 9 . Find the original number.
2. Mike and Dick are 30 km apart and they start running at the same time. If they run towards each other, they will meet after 3 hours. If they run in the same direction, Mike will catch up with Dick after 10 hours. Find the speed that each is running at.
有關Simultaneous Linear Equation
2012-02-12 6:07 pm
回答 (2)
2012-02-12 8:50 pm
✔ 最佳答案
1 Let the digit is 10x + y, theny = 2x...(1)10y + x = 2(10x + y) - 9...(2)Sub. (1) into (2)20x + x = 2(10x + 2x) - 921y = 24x - 9x = 3, y = 6The original number is 362 Let the speed of Mile and Dick are x and y km/h respectively.Then 3(x + y) = 30...(1)10(x - y) = 30...(2)From (1) y = 10 - x. Sub. into (2)10(x - 10 + x) = 302x = 13x = 6.5, y = 3.5The speed of Mile and Dick are 6.5 and 3.5 km/h respectively.
2012-02-12 6:56 pm
1)let x be the units digit of the number and y be the tens digit,then the original number is 10y + x, and the new number is 10x + y,from the question , we havex = 2y............(1)2(10y + x) - (10x + y) = 9...........(2)from (2) : 10x + 19y = 9................(3) ??? 2)let the speed of Mike be x km/h, and the speed of Dick be y km/hfrom the question , we have3(x+y) = 30 x+y =10 .........(1)10(x-y) = 30x- y = 3........(2)(1) + (2) :2x = 13x = 6.5sub. = 6.5 into (1)6.5 + y = 10y = 3.5therefore the speed of Mike be 6.5km/h and the speed of Dick be 3.5 km/h
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