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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation2.12 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.
 Q 1: The admission fee at a fair is \$1.50 for children and \$4.00 for the adults. On a certain day 2200 people attended the fair and \$5050 is collected. How many children and how many adults attended the fair? (Hint: c be the number of children attended and a be the number of adults attended, then we can write the algebraic equations: a + c = 2200, 4a + 1.5c = 5050)700 adults and 1500 children450 adults and 1200 children500 adults and 1400 children Q 2: A number is four less than two times another number. Their sum is two hundred. What are the numbers? (Hint: Let a be one number and b be another number. The equations: a=2b-4, a+b=200, Solve for a and b)a = 404 and b = 204a = 402 and b = 202a = 400 and b = 200 Q 3: If the larger of two numbers were decreased by 400, then the two numbers would be the same. The sum of the two numbers is 750. What are the numbers? (Hint: Let a be the small number and b be the large number. Then a = b - 400, a + b = 750, Solve for a and b) a = 170 and b = 575a = 165 and b = 565a = 175 and b = 575 Q 4: A number is nine less than six times another number. Their sum is 82. What are the numbers? (Hint: Let a be one number and b be another number. The equations: a=6b-9, a+b=82, Solve for a and b)a = 69 and b = 13a = 39 and b = 23a = 59 and b = 13 Q 5: One number is 2 more than three times another number. If each number were multiplied by three, their difference would be 42. What are the numbers? (Hint: Let a be one number and b be another number. The equations can be written as: a=3b+2 and 3a-3b=42 Substituting a in equation 2 and solve for a and b)a=20 and b=16a=10 and b=8a=20 and b=6 Q 6: A number is four less than two times another number. Their sum is 50. What are the numbers? (Hint: Let a be one number and b be another number. The equations: a=2b-4, a+b=50, Solve for a and b)a = 22 and b = 20a = 32 and b = 28a = 32 and b = 18 Q 7: If the larger of two numbers were decreased by sixty, then the two numbers would be the same. The sum of the two numbers is hundred. What are the numbers? (Hint: Let a be the small number and b be the large number. Then a = b - 60, a + b = 100, Solve for a and b) a = 50 and b = 110a = 60 and b = 100a = 45 and b = 90 Q 8: One number is four times another number. If each number were multiplied by two, their difference would be 54. What are the numbers? (Hint: Let a be one number and b be another number. The equations can be written as: a = 4b and 2a-2b=54. Solve for a and b)a = 26 and b = 19a = 16 and b = 9a = 36 and b = 9 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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