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

Method 2:
Step 1: Write all the equations in terms of one variable.
Step 2: Solve the equation

Example :
The tens digit of a two-digit number is two more than the ones digit. The number is thirty more than four times the sum of the digits. What is the number?

Solution:
Let the ones digit be 'x'
Tens digit is two more than the ones digit = x + 2
The number is 10(x+2) + x
Thirty more than four times the sum of the digits so 4(x + x + 2) +30
Therefore, the number is thirty more than four times the sum of the digits can be written as
10(x + 2) + x = 4(x + x + 2) + 30
10(x + 2) + x = 4(2x + 2) + 30
10x + 20 + x = 8x + 8 + 30
11x + 20 = 8x + 38
11x - 8x = 38 - 20
3x = 18
x = 18/3 = 6
the number in tens place is x + 2 = 6 + 2 = 8
The number is 86.

Directions: Solve the following word problems.

Name: ___________________

Date:___________________

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

Q 1: The sum of the digits of a two digit number is 8. If 18 is added to the number, the digits are reversed. Find the number.
(Hint: Let the digit is units place = x
Digit in the ten's palce = 8 - x
The number = 10(8 - x) + x
when the digits are reversed the number = 10x + (8 - x)
Solve the equation: 10(8 - x) + x + 18 = 10x + (8 - x) )
26
17
35

Q 2: Find the number whose half diminished by 1 is equal to one third of the number. (Hint: Let the number be x.
number whose half diminished by 1 is equal to one third of the number can be written as: (1/2)x - 1 = (1/3)x
Solve for x)
9
6
8

Q 3: The difference between ten's digit and unit's digit of a two digit number is 6. When the digits are reversed the new number added to the original number becomes 88. Find the original number.
(Hint: Let the units digit be x, then the ten's digit = x + 6
The number is 10(x + 6) + x
when the digits are reversed, the number is 10x + (x + 6)
Solving the equation: 10(x + 6) + x + 10x + (x + 6)= 88)
82
93
71

Q 4: The ten's digit of a two digit number exceeds the unit's digit by 4. The sum of the digits is 10. Find the number.
(Hint: Let the units digit = x
Ten's digit = x + 4
x + x + 4 = 10 )
40
73
51

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Question 6: This question is available to subscribers only!


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