To solve the problem of finding the sum of the digits of the product of [tex]\(A = 7777777 \times 999999999\)[/tex], we need to follow a series of steps. Let’s go through them step-by-step:
1. Step 1: Calculate the Product
- First, we need to find the product of [tex]\( 7777777 \)[/tex] and [tex]\( 999999999 \)[/tex].
2. Step 2: Identify the Product
- The product of [tex]\( 7777777 \)[/tex] and [tex]\( 999999999 \)[/tex] is [tex]\( 7777776992222223 \)[/tex].
3. Step 3: Convert the Product to Individual Digits
- Next, we separate the product [tex]\( 7777776992222223 \)[/tex] into its individual digits:
[tex]\[
7, 7, 7, 7, 7, 7, 6, 9, 9, 2, 2, 2, 2, 2, 2, 3
\][/tex]
4. Step 4: Sum the Digits
- We now add all the individual digits together:
[tex]\[
7 + 7 + 7 + 7 + 7 + 7 + 6 + 9 + 9 + 2 + 2 + 2 + 2 + 2 + 2 + 3
\][/tex]
- Performing the addition step-by-step:
[tex]\[
(7+7+7+7+7+7) + 6 + 9 + 9 + (2+2+2+2+2+2) + 3
\][/tex]
[tex]\[
42 + 6 + 9 + 9 + 12 + 3
\][/tex]
[tex]\[
42 + 6 = 48
\][/tex]
[tex]\[
48 + 9 = 57
\][/tex]
[tex]\[
57 + 9 = 66
\][/tex]
[tex]\[
66 + 12 = 78
\][/tex]
[tex]\[
78 + 3 = 81
\][/tex]
5. Step 5: Confirm the Result
- After summing up all the individual digits of the product, the total sum is [tex]\( 81 \)[/tex].
Thus, the sum of the digits of the product [tex]\( 7777777 \times 999999999 \)[/tex] is:
[tex]\[
\boxed{81}
\][/tex]
So, the correct answer is:
[tex]\[
e) 81
\][/tex]
