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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
3.17 Word Problems - Digit - 2

Example:
If twenty-seven is added to a two-digit number, the original number will be reversed. The number is three less than four times the sum of its digits. What is the number?

Solution:
Let 'u' be the number in the units place and 't' be the number in the tens place.
The number can be written as 10t + u
If twenty-seven is added to a two-digit number, the original number will be reversed: 10t + u + 27 = 10u + t
The number is three less than four times the sum of its digits: 10t + u = 4(t + u) - 3
10t + u + 27 = 10u + t -----------equation 1
10t + u = 4(t + u) - 3-------------equation 2
10t + u + 27 = 10u + t ----------- equation 1
10t - t = 10u - u - 27
9t = 9u - 27
t = u - 3
10t + u = 4(t + u) - 3 ----------- equation 2
10t + u = 4t + 4u - 3
6t = 3u - 3
substituting t = u - 3 in the above equation we have
2(u - 3) = u - 1
2u - 6 = u - 1
u = 6 - 1 = 5
t = u - 3 = 5 - 3 = 2
The two digit number is 25

Verification:
If twenty-seven is added to a two-digit number, the original number will be reversed:
25 + 27 = 52
52 is a reverse of 25
The number is three less than four times the sum of its digits 4(2+5)-3 = 4(7) - 3 = 28 - 3 = 25
Directions: Solve the following word problems.
Q 1: The tens digit is 2 less than the units digit. If the digit are reversed, the sum of the reversed number and the original number is 154. Find the original number.
84
76
68

 Q 2: If 9 is added to a two digit number, the number is reversed. If you subtracted 7 from the number, you will get 5. Find the number.
(Hint: Let u be the number in the units place, t be the number in the tens place. The two digit number can be written as 10t + u. If it is reversed it can be written as 10u + t.
If 9 is added to a two digit number, the number is reversed can be written as 10t + u + 9 = 10u + t.
If you subtracted 7 from the number, you will get 5 can be written as 10t + u - 7 = 5.
Solving both equation for t and u, find the number.)
13
9
12

Q 3: The ratio of the units digit to the tens digit of a two digit number is one half. The tens digit is 2 more than the units digit. Find the number.
42
65
36

 Q 4: If you switch the ones digit by the tens digit, the sum of the 2 numbers will be 55. The ones digit is 3 more that the tens digit. What is the number. (Hint: Let u be the number in the units place and t be the number in the tens place. The number can be written as 10t + u. If the number is reversed then it will be 10 u + t. The sum of the number and its switch equals 55 implies 10t + u + 10u + t = 55. The other equation can be written as u = 3 + t. Solve both equations to find u and t and the number.)
14
25
41

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