Word Problems: Solving for Unknown Numbers - Prof. Errin E. White, Assignments of Algebra

A collection of word problems that involve solving for unknown numbers using various mathematical operations such as addition, subtraction, multiplication, and division. The problems range from simple equations to more complex ones, and their solutions are provided at the end of the document.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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Word Problems
E. White
(1) Twice a number plus 3 equals thirty-nine.
(2) A number plus four times the same number equals 30, find the number.
(3) A number minus three times the same number equals 12, what is the number.
(4) Three times a number plus one-half equals the number plus 2.
(5) A number minus 11 equals 12 minus the number.
(6) If four is subtracted from a certain number, the result is the same as adding three to twice the number.
(7) A number plus seven equals twice the number minus five, what is the number?
(8) Three less than four times a certain number is twelve, what is the number?
(9) If 11 is subtracted from twice a number one gets 7. Find the number.
(10) Half of a certain number plus 3 gives the same value as twice the number plus 7. What is the number?
(11) If 2 is subtracted from a number the result is the same as when five is added to the number doubled. What is
the number?
(12) Find a number such that three less than four times the number is two less than the number plus eight.
(13) Two-thirds of a number plus three-fifths of a number is 1, find the number.
(14) One-fourth less than two-thirds of number equals the number minus 4. What is the number?
(15) If a certain number is subtracted from ten the result is the same as if five is subtracted from twice the number.
What is the number?
(16) The sum of three consecutive integers is 54, find the integers.
(17) Ten times the larger of two consecutive even integers minus seven times the smaller equals two times the sum
of the two integers. Find the integers.
(18) Four times the larger of two consecutive odd integers is seven less than five times the smaller. What are the
integers?
(19) The smallest plus the largest of three consecutive odd integers is twelve less than six times the middle integer.
Find the smallest of the integers.
(20) Three times the middle integer of three consecutive integers equals four less than twice the sum of the smallest
and largest, find the integers.
(21) One-third the middle number of three consecutive integers plus six equals one-half the smallest plus one-sixth
the largest, what are the integers?
(22) Eight minus the smaller of two numbers is one less than the larger of two numbers. If their difference is 1,
what are the numbers?
(23) The number seven divided by a number equals the number 5 divided by the sum of the number and 1. What
are the numbers?
(24) The sum of two numbers is twelve while their difference is 15. What are the numbers?
(25) Thirty-six minus the sum of two numbers is three, while their difference is 5. Find the numbers.
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Word Problems

E. White (1) Twice a number plus 3 equals thirty-nine.

(2) A number plus four times the same number equals 30, find the number.

(3) A number minus three times the same number equals 12, what is the number.

(4) Three times a number plus one-half equals the number plus 2.

(5) A number minus 11 equals 12 minus the number.

(6) If four is subtracted from a certain number, the result is the same as adding three to twice the number.

(7) A number plus seven equals twice the number minus five, what is the number?

(8) Three less than four times a certain number is twelve, what is the number?

(9) If 11 is subtracted from twice a number one gets 7. Find the number.

(10) Half of a certain number plus 3 gives the same value as twice the number plus 7. What is the number?

(11) If 2 is subtracted from a number the result is the same as when five is added to the number doubled. What is the number?

(12) Find a number such that three less than four times the number is two less than the number plus eight.

(13) Two-thirds of a number plus three-fifths of a number is 1, find the number.

(14) One-fourth less than two-thirds of number equals the number minus 4. What is the number?

(15) If a certain number is subtracted from ten the result is the same as if five is subtracted from twice the number. What is the number?

(16) The sum of three consecutive integers is 54, find the integers.

(17) Ten times the larger of two consecutive even integers minus seven times the smaller equals two times the sum of the two integers. Find the integers.

(18) Four times the larger of two consecutive odd integers is seven less than five times the smaller. What are the integers?

(19) The smallest plus the largest of three consecutive odd integers is twelve less than six times the middle integer. Find the smallest of the integers.

(20) Three times the middle integer of three consecutive integers equals four less than twice the sum of the smallest and largest, find the integers.

(21) One-third the middle number of three consecutive integers plus six equals one-half the smallest plus one-sixth the largest, what are the integers?

(22) Eight minus the smaller of two numbers is one less than the larger of two numbers. If their difference is 1, what are the numbers?

(23) The number seven divided by a number equals the number 5 divided by the sum of the number and 1. What are the numbers?

(24) The sum of two numbers is twelve while their difference is 15. What are the numbers?

(25) Thirty-six minus the sum of two numbers is three, while their difference is 5. Find the numbers.

Answers: (1) 2 x + 3 = 39 ; 18 (2) x + 4x = 30 ; 6 (3) x − 3 x = 12 ; − 6 (4) 3 x + 12 = x + 2 ;

3 4

(5) x − 11 = 12 − x ;

(6) x − 4 = 2x + 3 ; − 7 (7) x + 7 = 2x − 5 ; 12 (8) 4 x − 3 = 12

;

4 (9)^2 x^ −^ 11 = 7 ; 9^ (10)^

x 2 + 3 = 2x^ + 7 ;^ −^

3 (11)^ x^ −^ 2 = 2x^ + 5 ;^ −^7 (12)^4 x^ −

3 = x + 8 − 2 ; 3 (13) 2 3

x +^3 5

x = 1 ; 15 19

x − 1 4

= x − 4 ; 45 4

(15) 10 − x = 2x − 5 ; 5

(16) x + (x + 1) + (x + 2) = 54 ; 17 , 18 , 19 (17) 10(x + 2) − 7 x = 2(x + (x + 2)) ; 16 , 18 (18) 4(x + 2) =

5 x − 7 ; 15 , 17 (19) x + (x + 4) = 6(x + 2) − 12 ; 1 (20) 3(x + 1) = 2(x + (x + 2)) − 4 ; 3 , 4 , 5

(21)

(x + 1) + 6 =

x +

(x + 2) ; 18 , 19 , 20 (22) 8 − S = L − 1 , L − S = 1 ; 4 , 5 (23)

x

x + 1

; −

2 (24)^ x^ +^ y^ = 12 ,^ x^ −^ y^ = 15 ;^ −^

2 (25)^36 −^ (x^ +^ y) = 3 ,^ x^ −^ y^ = 5 ; 14, 19