if NR+RN=ABC where A,B,C,N and R are digits what is maximum value of B+C?
78
+87
-----------
165
N= 7
R=8
A=1
B=6
C=5
B+C=11
99+99 = 198
B+C = 17
The only way you could get more than that would be if the number ended in 99.
But NR+RN = 11(R+N) so R+N would have to end in 99. I think you can see why that cannot be so.
Why did the number throw a party? Because it was feeling "prime"! Now, let's solve this mathematical riddle, shall we?
Given NR + RN = ABC, where A, B, C, N, and R are digits, we need to find the maximum value of B + C.
Hmm... let's see. Since A, B, C, N, and R are digits, they can only take on values from 0 to 9. Therefore, to find the maximum value of B + C, we should find what values will result in the maximum sum.
Let's think about the digits involved. The numbers NR and RN, when added together, result in a three-digit number ABC. Now, if we want to maximize B + C, we should choose the largest possible values for B and C.
Since B is the tens digit and C is the units digit, to get the highest possible sum, we want B to be as large as possible and C to be as small as possible.
Considering this, the maximum value for B is 9 (the largest possible digit), and the smallest value for C is 0 (the smallest possible digit). So, the maximum value of B + C would be 9 + 0 = 9.
Therefore, the maximum value of B + C in the equation NR + RN = ABC is 9. Enjoy the math puzzle!
To find the maximum value of B + C in the equation NR + RN = ABC, we need to determine the maximum values for B and C.
Since A, B, C, N, and R are digits, they will have values between 0 and 9.
First, let's consider the possible values for R and N:
- R can be any digit from 0 to 9.
- N can be any digit from 0 to 9, excluding the one chosen for R.
Now, let's find the values for B and C that maximize their sum B + C.
If B is the largest possible digit 9, then C must be 8 in order to maximize their sum. In this case, B + C = 9 + 8 = 17.
Therefore, the maximum value of B + C in the equation NR + RN = ABC is 17.
To find the maximum value of B + C in the equation NR + RN = ABC, we need to consider the possible values for A, B, C, N, and R.
Let's analyze the equation step by step:
First, notice that NR + RN can be written as 10N + R + 10R + N, which simplifies to 11N + 11R.
So, the equation becomes 11N + 11R = ABC.
Now, let's consider the possible values for N and R. Since A, B, C, N, and R are digits, they can only take values from 0 to 9.
Let's substitute the maximum values for N and R, which are both 9, into the equation:
11(9) + 11(9) = ABC
99 + 99 = ABC
198 = ABC
The maximum possible value for ABC is 198.
Now, we need to find the maximum value for B + C. Since A, B, and C are digits, B and C can only take values from 0 to 9.
To find the maximum value of B + C, we need to find the value of B and C that maximizes their sum while being consistent with the equation ABC = 198.
By trying different combinations, we find that B = 9 and C = 9 is the combination that gives the maximum sum.
Therefore, the maximum value of B + C in the equation NR + RN = ABC is B + C = 9 + 9 = 18.