Question 522973
the difference of digits of two digit number is 1.
five times the sum of the number plus one is equal to the number.
 find the number
:
Two digits, a, b
then
10a + b = the number
:
"the difference of digits of two digit number is 1."
a - b = 1
:
"five times the sum of the number plus one is equal to the number."
5(a+b) + 1 = 10a + b
5a + 5b + 1 = 10a + b
5a - 10a + 5b - b = -1
-5a + 4b = -1
:
Use substitution here, multiply the 1st equation by 4, add to the 2nd eq
+4a - 4b = 4
-5a + 4b = -1
--------------addition eliminates b, find a
-a = 3
a = -3
find b
-3 - b = 1
-b = 1 + 3
-b = 4
b = -4
:
The number
-3(10) + (-4) = -34 is the number
:
:
Usually not a neg answer in these problems, see if this works in the statement:
"five times the sum of the number plus one is equal to the number."
5(-3 + (-4)) + 1 = -34
5(-7) + 1 = -34
-35 + 1 = -34; confirms our solution of -34