A two-digit number has the property that the square of its tens-digit plus ten times its units digits equals the square of its units digit plus ten times its tens digit. Write the sum of the smallest three two-digit numbers, which have this property, and are prime numbers
Answers
Answer:
let T equal the tens digit.
let U equal the units digit.
you are given that the sum of its digits is 3 times its units digit.
this translates to the following equation:
T + U = 3 * U
you are also given that its tens digit exceeds its units digit by 4.
this translates to the following equation:
T = U + 4
from these relationships, you can figure out what value each of the digits is.
since T = U + 4, you can replace T with U + 4 in the first equation of T + U = 3 * U.
T + U = 3 * U becomes:
(U + 4) + U = 3 * U
simplify this equation to get:
U + 4 + U = 3 * U
combine like terms to get:
2 * U + 4 = 3 * U
subtract 2 * U from both side of this equation to get:
4 = U
the units digit is equal to 4.
from the equation T = U + 4, you can solve for T to get:
T = 4 + 4 = 8
you now have:
T = 8
U = 4
that's your solution.
it translates to:
the tens digit is equal to 8 and the units digit is equal to 4.
you can confirm by using those values in the original problem statement to see if the original problem statement is true.
the original problem statement is:
A two digit number the sum of its two digits is three times of its units digit and its tens digit exceeds its units digit by 4.
the 2 digit number is 84.
the sum of 8 and 4 is equal to 12 which is 3 times the unit digit of 4.
the tens digit is 8 which exceeds the unit digit of 4 by 4.
both problem statements are true when you assume 8 for the tens digit and 4 for the units digit so that's your answer.
Answer:
A two-digit number has the property that the square of its tens-digit plus ten times its units digits equals the square of its units digit plus ten times its tens digit. Write the sum of the smallest three two-digit numbers, which have this property, and are prime numbers