Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation 2.12 Linear Equation - Two Variables - Word Problems
Example 1:
One number is 28 more than three times another number. If each number were multiplied by four, their difference would be 232. What are the numbers? Solution:
a =3b +28
4a - 4b = 232
a = ? b = ?
4a - 4b = 232
4(3b +28) - 4b = 232
12b + 112 - 4b = 232
8b + 112 = 232
8b = 232 - 112
8b = 120
b = 120/8 = 15 =>b = 15
a = 3b +28 = 3(15) + 28 = 45 + 28 = 73 => a =73 Example 2: Solution:
A number is three less than four times another number. Their sum is two hundred and seven. What are the numbers?
a = 4b-3 ----- equation 1
a + b = 207 --- equation 2
substituting a = 4b-3 in equation 2 we have
a + b = 207
(4b-3) + b = 207
4b - 3 + b = 207
5b - 3 = 207
5b - 3 + 3 = 207 + 3
5b = 210
b = 210/5 = 42 => b = 42
a = 4b - 3 = 4(42) - 3 = 168 - 3 = 165 =>a = 165 Example 3:
If the larger of two numbers were decreased by three hundred forty-nine, then the two numbers would be the same. The sum of the two numbers is 735. What are the numbers? Solution:
a = b - 349
a + b = 735
(b - 349) + b = 735
b - 349 + b = 735
2b - 349 + 349 = 735 + 349
2b = 1084 b = 542
a = b - 349 = 542 - 349 =193 a = 193 Directions: Solve the following questions.