SOLUTION: the tens digits of a certain number is 7 less than the units digit .the sum of the squares of the two digits is 85.find the number.with justification
Algebra.Com
Question 1146571: the tens digits of a certain number is 7 less than the units digit .the sum of the squares of the two digits is 85.find the number.with justification
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
t = the tens digit
u = the units
:
Write an equation for each statement
:
the tens digits of a certain number is 7 less than the units digit.
t = u - 7
the sum of the squares of the two digits is 85.
t^2 + u^2 = 85
replace t with (u-7)
(u-7)^2 + u^2 = 85
FOIL(u-7)(u-7)
u^2 - 14u + 49 + u^2 - 85 = 0
2u^2 - 14u - 36 = 0
simplify divide 2
u^2 - 7u - 18 = 0
Factors to
(u-9)(u+2) = 0
the positive solutin
u = 9
then
t = 9 - 7
t = 2
find the number.with justification
Number is 29
:
:
Check: 2^2 + 9^2 = 81 + 4 = 85
RELATED QUESTIONS
The tens digit of a certain number is 7 less than the units digit. The sum of the squares (answered by checkley77)
the tens digits of a certain number is 7 less than the units digit .the sum of the... (answered by Edwin McCravy)
the tens digits of a certain number is 7 less than the u digit .the sum ofnits the... (answered by richwmiller,josgarithmetic)
The units digit of a two-digit number is 2 less than the tens digit. The sum of the... (answered by JulietG)
The tens digit of a certain number is 3 more than the units digit. The sum of the squares (answered by bucky)
The sum of the digits of a two-digit number is 13. Twice the tens digit is two less than... (answered by josgarithmetic)
The sum of the digits of a two-digit number is 13. The tens digit is seventeen
less... (answered by ikleyn,josgarithmetic)
A two digit number is two less than six timers the sum of its digits. The tens digit is... (answered by Paul)
the sum of the digits of a 2-digit number is 7. The tens digit is one less than 3 times... (answered by Mathtut)