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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
3.15 Story Problems - Digits

Digit problems are problems involving numbers with two or more digits.

Example:
89
8 tens or 8 x 10 = 80
9 units or 9 x 1 = 9
Sum = 89
The number is expressed as 10t + u, where t is the digit in the tens place and u is the digit in the units place.
Example:
456
4 one hundreds or 4 x 100 = 400
5 tens or 5 x 10 = 50
6 units or 6 x 1 = 6
Sum = 456
The number is expressed as 100h + 10t + u, where h is the digit in the hundreds place and t is the digit in the tens place and u is the digit in the units place.

Method 1:
Example:
The sum of the digits of a two-digit number is 4. The ones digit is three times the tens digit. What is the number?
Solution:
Let 'u' be the digit in the units place and 't' be the digit in the tens place.
t + u = 4
u = 3t
substituting u = 3t in t + u = 4
t + u = 4
t + 3t = 4
4t = 4
t = 1
u = 3t = 3x1 = 3
The number is 13

Example:
The sum of the digits of a two digit number is 7. When the digits are reversed, the number is increased by 27. Find the number?
Solution:
Let 'u' be the number in the units place and 't' be the number in the tens place.
The algebraic equations can be written:
The sum of the digits of a two digit number is 7 as t + u = 7
The digits are reversed can be written as 10u + t.
When the digits are reversed, the number is increased by 27 can be written as 10u + t = 10t + u + 27.
Solving for t and u:
t + u = 7
t = 7 - u
10u + t = 10t + u + 27
10u + 7 - u = 10(7 - u) + u + 27
10u + 7 - u = 70 - 10u + u + 27
9u + 7 = -9u +97
18u = 97 - 7
18u = 90
u = 90/18 = 45/9 = 5
t = 7 - u = 7 - 5 = 2
So the number has units place 5 and tens place 2 therefore the number is 25
Answer: 25

Directions: Solve the following word problems.
Q 1: The tens digit of a certain number is 5 more than the units digit. The sum of the digits is 9. Find the number.
48
72
65

Q 2: Eight times the sum of the digits of a certain two digit number exceeds the number by 19. The tens digit is 3 more than the units digit. Find the number.
45
85
67

Q 3: The sum of the digits of a three digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals the sum of the other two. Find the number.
231
132
123

Q 4: The units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
92
48
54

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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