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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: If the larger of two numbers were decreased by fifty eight, then the two numbers would be the same. The sum of the two numbers is two hundred and twenty two. What are the numbers? (Hint: Let a be the small number and b be the large number. Then a = b - 58, a + b = 222, Solve for a and b) a = 82 and b = 140a = 81 and b = 100a = 48 and b = 90 Q 2: 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 = 60 and b = 100a = 50 and b = 110a = 45 and b = 90 Q 3: 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 = 36 and b = 9a = 26 and b = 19a = 16 and b = 9 Q 4: 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 = 32 and b = 28a = 32 and b = 18a = 22 and b = 20 Q 5: 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 6: A number is five less than four times another number. Their sum is 65. What are the numbers? (Hint: Let a be one number and b be another number. The equations: a=4b-5, a+b=65, Solve for a and b)a = 51 and b = 14a = 65 and b = 14a = 51 and b = 65 Q 7: 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 8: 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 = 400 and b = 200a = 402 and b = 202 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!