each letter stands for a different digit. If WAIT = 8472, what number does STOP reporesent?
GO
+SLOW
_______
STOP
To solve this problem, we need to assign unique digits to each letter to form a correct addition. Given that "WAIT" equals 8472, we know that W=8, A=4, I=7, and T=2. We can use these values to find the value of the letters in "STOP."
First, let's assign temporary values for the unknown digits in "SLOW" as follows:
G = _
S = _
L = _
O = _
Now, let's solve the addition:
G O
+ S L O W
_________
S T O P
By observing the addition, we can determine the following:
1. The sum of the units place (O + W) equals P. But since W=2, and O + 2 = P, we know that O + 2 must equal P.
2. The sum of the tens place (S + L + T) equals O. But since L is a different digit, T is 2, and S + 2 = O, we know that S + 2 must equal O.
Now, let's update the representation of "STOP":
G 2
+ S L 2
_________
S T O P
3. The sum of the hundreds place (G + O + O) equals T. But since G is a different digit and we have already assigned T = 2, we know that 8 + O + 2 = 2. This means that O must be 2.
Now, let's update the representation of "STOP":
G 2
+ S L 2
_________
S T 2 P
4. Since O = 2, we know that S + 2 = O, so S must be 0.
Now, let's update the representation of "STOP":
G 2
+ 0 L 2
_________
0 T 2 P
5. Since T = 2 and the only remaining digit is G, we know that G must be 9.
Now, let's update the representation of "STOP":
9 2
+ 0 L 2
_________
0 2 2 P
Based on our deductions, we can conclude that in "STOP," G=9, S=0, L can be any digit, O=2, and P can be any digit.
Therefore, "STOP" can represent any number in the form 9022P.
To find the value of each letter in the equation GO + SLOW = STOP, we can use logical deduction.
First, let's analyze the information given: WAIT = 8472.
From this, we can conclude the following:
W = 8
A = 4
I = 7
T = 2
Now, let's analyze the equation GO + SLOW = STOP.
Since each letter stands for a different digit, we need to find the value of G, O, S, and L.
Let's start with G:
There is no carrying involved when adding T + O, so G + S must be less than or equal to 10.
The only single-digit number left is 1 (since 0 is used for T), so G must equal 1.
Now, let's move on to S:
Carrying is involved when adding O + L, so G + S must be greater than or equal to 10.
Since G is 1, S must be 9 to satisfy this condition.
Now we can calculate O:
From the equation: T + O = 2
Since T = 2 (from WAIT = 8472) and O + T = 2, O must be 0.
Finally, let's calculate L:
Carrying is involved when adding G + S, so L + O must be 0.
Since O is 0, L must be 0.
Now we have determined the value of each letter:
G = 1
O = 0
S = 9
T = 2
L = 0
Therefore, STOP represents the number 1902.