Math Problem....

[KennyB]

I can look at this problem, and see the answer, but I can't figure out how to solve it.

Adam calls a hardware store and orders a certain length of rope in feet and inches. The store clerk gets this backwards and reverses the lenght, switches feet and inches. When Adam goes to pick the rope up it is 9'2" too short. What is the original length of rope that Adam ordered?

If you can help me set this up, I would appreciate it, it's driving me crazy.

[FreeMarketeer]

Assuming integer values of feet and inches, there is no unique solution. Rather, there are two possible solutions. However, since one of them involve one of the digits being zero, the most likely solution is 11'1" (the other is 10'0").

TO set it up, just call the number of feet x, and the number of inches y. Create an equation that looks like this:

12X + 4 - (9x12 + 2) = 12Y + X

Solve for Y as a function of X:

Y = X - 10

Obviously, neither X nor Y can be less than zero, and neither can be greater than 11. There are two possible solutions, 11'1" and 10'0".

1'11" is 9'2" shorter than 11'1", and 0'10" is 9'2" shorter than 10'0".

[KennyB]

Okay, when I solve it, I get just the 10'0", I know 11'1" is the correct answer, but I can't get it to work out.

[jay_shark]

Lets convert the length of the rope in inches .
12inches =1foot

x'y''=12x+y (original length)
y'x''= 12y +x

However it is known that the rope was short by 9'2'' which when we convert to inches becomes 110 inches .

110 + 12y + x = 12x +y
110=11x-11y
10=x-y

(10,0) (11,1) (12,2)(13,3) etc . 0<=y<=12