uncle richard's phone number contains 8 different numbers. The sum of the numbers formed by the first 5 digits and the number formed by the last 3 digits is 68427. The sum of the number formed by the first 3 digits and the number formed by the last 5 digits is 36090. what is the uncle's phone number
your brother is at the hospital. will you come to my house.
a b c d e f g h
first 5 = e+10 d + 100 c + 1000 b + 10,000 a
last 3 = 100 f + 10 g + h
sum = 10,000 a + 1000 b + 100(c+f) + 10(d+g) + (e+h)
so
a = 6
b = 8
c + f = 4
d + g = 2
e + h = 7
===================
first three = 100 a + 10 b + c
last five = 10,000 d + 1,000 e + 100 f + 10 g + h
sum = 10,000 d + 1000 e + 100(a+f) + 10(b+g) + (c+h) = 36090
so
d = 3 , e = 6 , a+f= 0 , (b+g) = 9 , (c+h )= 0
so
a = 6
b = 8
c = ?
d = 3
e = 6
f = ?
g = ?
h = ?
well a + f ends in 0 and a = 6 so f = 4
c + f = 4 so c = 0
c+ h = 0 so h = 0
b + g = 9 so g = 1
6 8 0 3 6 4 1 0
I did that fast, check it! Particularly where a 1 should be carried left
To find Uncle Richard's phone number, we need to analyze the information given and solve for the individual digits.
Let's assume the phone number has the following format: ABCDEFGH, where A, B, C, D, E, F, G, and H represent different digits.
From the first statement, we know that A + B + C + D + E + F = 6842(7).
And from the second statement, we know that A + B + C = 3609(0).
We can subtract the second statement from the first statement to get (A + B + C + D + E + F) - (A + B + C) = 6842(7) - 3609(0).
This simplifies to (D + E + F) = 3241(7) - 3609(0).
By subtracting the right side, we find that (D + E + F) = 3258(7).
Since the sum of three different digits cannot be greater than 9 + 8 + 7 = 24, it means that the missing digit G must be 1.
Now, we have the equation (D + E + F) + 1 = 3258(7).
By subtracting 1 from both sides, we find (D + E + F) = 3258(7) - 1.
By calculating this subtraction, we have (D + E + F) = 22807.
Now, we need to find three different digits whose sum is equal to 22807.
To find these digits, we simply need to list all the possible combinations that add up to 22807, considering no digit can be repeated.
After computing all possible combinations, we find that the only combination with different digits that works is 9 + 7 + 8 = 24.
Therefore, D = 9, E = 7, and F = 8.
Now, we have the phone number AB9E7G81.
We also know from the second statement that A + B + 9 = 3609(0).
Subtracting 9 from both sides, we get A + B = 3609(0) - 9.
By calculating this subtraction, we find A + B = 36081.
Lastly, we need to find two different digits whose sum equals 36081.
Again, we list all the possible combinations, which gives us 9 + 0 = 9.
Therefore, A = 9 and B = 0.
Putting it all together, Uncle Richard's phone number is 9079781.