I have an equation
..MEAT
+TEAM
STEAM
Different letters can have same values, but same letters can't have different numerical values. They are also only 1 digit numbers.
Can you help me confirm that the equation written above is an impossible situation for any values of S, T, E, A, and M?
I figured that if A+A=A, it can only either be 0 or 9 with a 1 carried over, but then T and M would have to be 0 and that is not allowed because it won't look like a number if I had a 0 digit in the front, like 0789. So, now I found out that A had to be 9. E is the same situation as A so it also has to be 9. S has to be 1 because it is the second digit of the sum of two 1 digit numbers. So M+T+1=1T considering T is a digit. Since it is a 1 digit number, M+1=10. M is 9. If M were 9, T could only be 0, which I said isn't allowed because it would be a number with a 0 in front.
If you think my way of approaching this wrong, please help find an example.
If you agree, tell another way to know.
2007-05-20 12:10:45 · 5 answers · asked by UnknownD 6 in Science & Mathematics ➔ Mathematics
It works for the trivial case of s,t,e,a,m all = 0. Writing out the equation of 10000s + 1000t + 100e + 10a + m = 1001m + 200e + 20a + 1001t allows us to get rid of some stuff on each side of the equation.
10000s -1000m - 100e -10a - t = 0
Since there are only 1's and zeros in each portion, none of those numbers can ever be big enough to override the next bigger value.
This equation shows very simply that no matter what range of values you pick for any letter, as long as they are limited to 1 digit values, meat is never big enough to take 10000 away from s. the maximum value of MEAT is 9,999 so the maximum value of (-1000m -100e-10a-t) is -9,999. Unless we can choose 0 for s, then we can't find an answer.
2007-05-20 12:38:16 · answer #1 · answered by Bradley B 2 · 0⤊ 0⤋
T+M = M =>T = 0
A+A = A => A = 0
E+E = E => E = 0
M+T = T => M = 0
S = 0
The only possible solution is 0+0 = 0
2007-05-20 12:20:09 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋
Assume it is possible.
Rewrite the equation
STEAM - TEAM = MEAT
10,000*S = MEAT
There is no integer S such that 10,000 times S equals a four-digit number.
The equation is impossible to solve with the constraints imposed.
2007-05-20 12:38:16 · answer #3 · answered by Steve A 7 · 0⤊ 0⤋
I don't understand your question. Revise it somehow. Are you saying prove that it is impossible that MEAT + TEAM = STEAM?
If so, since T + M = M, it is clear that T = 0 or 10. This is impossible. Thank you. :)
2007-05-20 12:17:42 · answer #4 · answered by Bob R. 6 · 0⤊ 0⤋
The New York Meats can really cook up some steam.
2007-05-20 12:28:35 · answer #5 · answered by Walter 5 · 0⤊ 0⤋