11. 12 = +10 2 = 1 (10) + 2 (1)
36 = 30 + 6 =
==
(10)
(10)
3
2
+
+
(1)
(1)
6
77+2027
units digittens digit
Consider the following analysis:
Let t = tens digit
u = units digit
ut +10two-digit number =
12. 12
36
27
For the sum of the digits of these two-digit, we have
⇒
⇒
⇒
1 + 2 =
6
7
3
3
2
+
+
=
=
9
9
t u
What if we reverse the digits of the two-digit numbers
given above, how are we going to write the new numbers
in terms of the variables t and u?
How are we going to
write the sum of these
two-digit numbers in
terms of the variables t
and u?
ut +
tu +10
13. Why do we need to know how
to write a two-digit number,
or the reverse of it, or the
sum of the digits of these
two-digit problems in terms
of the variables t and u?
14. Word Problem Number 1:
The units digit of a two-digit number
exceeds the tens digit by 2. Find the number
if it is 4 times the sum of its digits.
Step 1: Assign a variable to the unknown
Let Tens digitx
2+x
( )210 ++ xx
( )2++ xx
=
=
=
=
Step 2: Form the Equation
( ) ( )[ ]24210 ++=++ xxxx
Units digit
Sum of its digit
Two-digit number
16. 2=x
Substitute the value of x to equation
( )210 ++ xx ( ) ( )22210 ++=
420 +=
24=
∴ The two-digit number is 24.
17. Word Problem Number 2:
The sum of the digits of a three-digit
number is 15. the tens digit is less than the
units digit by 3. If the digits are reverse, the
new number diminish by 78 is three times the
original number. Find the original number.
Step 1: Let x
3−x
( )315 −+− xx
( )[ ] ( ) xxxx +++−+− 310315100
( ) ( )[ ]315310100 −+−+−+ xxxx
( ) ( )[ ] ( )[ ] ( ){ }xxxxxxxx +−+−+−=−−+−+−+ 310315100378315310100
=
=
=
=
=
Tens digit
Units digit
Hundreds digit
Original number
New number
Step 2:
20. How do we solve a digit problem?
We solve a digit problem by
first assigning variables to the
unknown, then after that forming
the equation basing on what is
asked in the problem. Then
simplify.
21. EXERCISES:
The sum of the three-digit number is 15.
The tens digit is less than the units digit by
two. If the digits are interchange the new
number decrease by 7 is twice the original
number. Find the original number.
A two-digit number and the resulting
number when the digits are reversed are
in the ratio 2:9. If the sum of the digits is 9,
find the original number.
The tens digit of a two-digit number is
twice its units digit. If the sum of the digits
is 12, what is the number?
1.
2.
3.
22. The sum of a two-digit number is 11. If the digit
are reversed, the new number increased by 20
is twice the original number. Find the number.
The hundreds digit of a three-digit number is
the sum of the tens and units digit, and the
units digit exceeds the tens digit by 2. Find the
number if it is 52 times the sum of its digit.
The units digit of a number exceeds twice its
tens digit by 3. if the digits are reversed, the
new number is 54 more than the original
number. Find the original number.
Solve the following.
1.
2.
3.
