Solving digit problems
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The document provides examples of solving digit problems by assigning variables to represent unknown digits, forming equations based on the information provided, and solving the equations to find the original numbers. It also provides exercises for the user to practice solving additional digit problems.
![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](https://image.slidesharecdn.com/solvingdigitproblems-160820074648/85/Solving-digit-problems-14-320.jpg)
![Step 3: Simplify the Equation
88 += x
( ) ( )[ ]24210 ++=++ xxxx
( )224 +x
211 +x 88 += x2− 2−
x11 68 += x x8−x8−
63 =x3
1
( ) ( ) 3
1
2=x
210 ++ xx](https://image.slidesharecdn.com/solvingdigitproblems-160820074648/85/Solving-digit-problems-15-320.jpg)
![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:](https://image.slidesharecdn.com/solvingdigitproblems-160820074648/85/Solving-digit-problems-17-320.jpg)
![Step 3:
( ) ( )[ ] ( )[ ] ( ){ }xxxxxxxx +−+−+−=−−+−+−+ 310315100378315310100
( )xxxxxx +−+−=−−+−+ 301020018003782183010100
( )3215 −− x ( )x218100 −
( )x18917703 −=
90108 −x x5675310 −=90+ 90+
x108 x5675400 −= x567+
675
x567+
5400675
=
x
675
8=x
Substitute the value of x to equation
( ) ( )[ ]315310100 −+−+−+ xxxx ( ) ( )[ ]8381038815100 +−+−+−=
( ) ( ) 85102100 ++=
850200 ++=
258=](https://image.slidesharecdn.com/solvingdigitproblems-160820074648/85/Solving-digit-problems-18-320.jpg)
Solving digit problems
- 2. a. b. Five less than four times a number m m45− 54 −m Question No. 1
- 3. a. b. Twice a certain number increased by 21 gives 53. 53212 =+x 53221 =• x Question No. 2
- 4. a. b. A certain number diminished by two x−2 2−x Question No. 3
- 5. What is the solution for the equation ? a. b. 12 4 xx 4845 +=−
- 6. How do you get the solution? xx 4845 +=− ⇒ 448445 ++=+− xx x5 x412 +=x4− 12=x x4−⇒ ⇒
- 7. Do you want more example? YES NO
- 8. Solve the following equations. 12 3 = x ( ) 36924 =+− xx 1) 2) YES NO
- 9. Okay, what is the solution for the equation: 12 3 = x a. b . 36 26
- 10. a. b. ( ) 36924 =+− xx 27 45
- 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
- 15. Step 3: Simplify the Equation 88 += x ( ) ( )[ ]24210 ++=++ xxxx ( )224 +x 211 +x 88 += x2− 2− x11 68 += x x8−x8− 63 =x3 1 ( ) ( ) 3 1 2=x 210 ++ xx
- 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:
- 18. Step 3: ( ) ( )[ ] ( )[ ] ( ){ }xxxxxxxx +−+−+−=−−+−+−+ 310315100378315310100 ( )xxxxxx +−+−=−−+−+ 301020018003782183010100 ( )3215 −− x ( )x218100 − ( )x18917703 −= 90108 −x x5675310 −=90+ 90+ x108 x5675400 −= x567+ 675 x567+ 5400675 = x 675 8=x Substitute the value of x to equation ( ) ( )[ ]315310100 −+−+−+ xxxx ( ) ( )[ ]8381038815100 +−+−+−= ( ) ( ) 85102100 ++= 850200 ++= 258=
- 19. The three-digit number is 258.∴
- 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.
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