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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

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.
Q 1: 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 = 65 and b = 14
a = 51 and b = 65
a = 51 and b = 14

Q 2: 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)
450 adults and 1200 children
700 adults and 1500 children
500 adults and 1400 children

Q 3: 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 = 110
a = 60 and b = 100
a = 45 and b = 90

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 = 18
a = 22 and b = 20
a = 32 and b = 28

Q 5: 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 = 402 and b = 202
a = 400 and b = 200
a = 404 and b = 204

Q 6: 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 = 165 and b = 565
a = 175 and b = 575
a = 170 and b = 575

Q 7: 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 = 59 and b = 13
a = 39 and b = 23
a = 69 and b = 13

Q 8: 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=6
a=10 and b=8
a=20 and b=16

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Question 10: This question is available to subscribers only!


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