ALGEBRA
Prof. Howard Sorkin                   Contact
SUPPLEMENTARY SHEET 2
  NUMBER and CONSECUTIVE INTEGER PROBLEMS
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - To DOWNLOAD this page for PRINTING .
If you are unable to do this you need to first DOWNLOAD Adobe's Acrobat Reader.
To obtain it click on https://get.adobe.com/reader/otherversions/
. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Notes on Sets Supplementary Sheet 6 - Adding and Subtracting rational expressions with Unlike Denominators
Supplementary Sheet 1 - Sets: Union, Intersection, Complement
Supplementary Sheet 2 - Number and Consecutive Number Word prolems Supplementary Sheet 7 - Square Roots
Supplementary Sheet 3 - Perimeter and Coin Word Problems Investment and Mixture Word Problems
Supplementary Sheet 4 - Motion Problems
Supplementary Sheet 5 - Negative Exponents and Scientific Notation Quadratic Equations

. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (Note: You must know how to write a correct algebraic equation for each of the problems below.  If you do not write a correct algebraic equation for any of the Word Problems given to you on your Test you will not get credit for your problem even if you have the correct answer!)

CLICK HERE


for Word Problem Basics
Part I

CLICK HERE

for Word Problem Basics
Part II

"ONE IN TERMS OF THE OTHER"

CLICK HERE

for Word Problem Basics
Part III

"A TOTAL AND WE DO NOT KNOW THE PIECES"

GO TO CONSECUTIVE INTEGER PROBLEMS 
 

NUMBER PROBLEMS

1.
 When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number.  Find the number.
Solution to Number Problem 1
2.
 When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4.  Find the number.
Solution to Number Problem 2
3.

Eight times a number increased by 9 is the same as 15 more than 7 times the number. Find the number.
Solution to Number Problem 3

4.
 Thirty decreased by 6 times a number is the same as 16 more than the number.  Find the number.
Solution to Number Problem 4
5.
 When 6 times a number is increased by 11 the result is 16 less than 9 times the number.  Find the number.
Solution to Number Problem 5
6.
 One number is twice another number.  If the 12 is subtracted from the larger number the result is 7 more than the smaller number.  Find the numbers.
Solution to Number Problem 6
7.
 The larger of two numbers is 10 more than the smaller number.  Five times the larger number is 40 more than 6 times the smaller.  Find the numbers.
Solution to Number Problem 7
8.
 If 13 is added to a number and the sum is multiplied by 3, the result is 7 times the number decreased by 9.  Find the number.
Solution to Number Problem 8
9.
 The sum of two numbers is 57.  If the larger of two numbers is 9 less than twice the smaller, find the two numbers.
Solution to Number Problem 9
10.
 The total of two numbers is 35.  Four times the larger number is 4 less than five times the smaller number.  Find the two numbers.
Solution to Number Problem 10
11.
 A piece of lumber which is 55 inches long is cut into two parts such that 2 times the larger part will be 12 more than 5 times the smaller part.  How large are each of the pieces of lumber?
Solution to Number Problem 11
12.
 The larger of two numbers is 6 less than 3 times the smaller number.  Three times the larger number is 7 more than 4 times the smaller number.  Find the numbers.
Solution to Number Problem 13
13.
 The larger of two numbers is 7 times the smaller.  The larger number exceeds the smaller number by 42.  Find the numbers.
Solution to Number Problems 1 and 2
14.
 The smaller of two numbers is 18 less than the larger number.  If 5 times the larger number exceeds 4 times the smaller number by 100.  Find the numbers.
Solution to Number Problem 14
15.
 A piece of fabric 180 inches long is cut into two pieces such that 3 times the larger piece exceeds 4 times the smaller piece by 85 inches.  How large are the two pieces of fabric?
Solution to Number Problem 15

   
Answers: 
  1.   12     2.   3   3.   6   4.   2    5.   9
  6.   19 and 38   7.   10 and 20   8.   12   9.   22 and 35 10.   19 and 16
11.   14 in. and 41 in. 12.    5 and 9 13.   7 and 49 14.   28 and 10 15.   65 in. and 115 in.
 
 
 
 
   
CONSECUTIVE INTEGER PROBLEMS
CLICK HERE FOR VIDEO ON CONSECUTIVE INTEGERS
1.

Find two consecutive integers whose sum is 123.
Solution to Consecutive Integer Problem 1

2.
 Find two consecutive integers whose sum is 97.
Solution to Consecutive Integer Problem 2
3.
 Find three consecutive integers whose sum is 171.
Solution to Consecutive Integer Problem 3
4.
 Find three consecutive integers whose sum is 54.
Solution to Consecutive Integer Problem 4
5.
 Find two consecutive even integers whose sum is 54.
Solution to Consecutive Integer Problem 5
6.
 Find two consecutive even integers whose sum is 38.
Solution to Consecutive Integer Problem 6
7.
 Find three consecutive even integers whose sum is 84.
Solution to Consecutive Integer Problem 7
8.
 Find three consecutive even integers whose sum is 48
Solution to Consecutive Integer Problem 8
9.
 Find two consecutive odd integers whose sum is 128.
Solution to Consecutive Integer Problem 8
10.
 Find two consecutive odd integers whose sum is 36.
Solution to Consecutive Integer Problem 10
11.
 Find three consecutive odd integers whose sum is 75.
Solution to Consecutive Integer Problem 11
12.
 Find three consecutive odd integers whose sum is 45.
Solution to Consecutive Integer Problem 12
13.

Three consecutive odd integers are such that the sum of the first and the third is 70. Find the integers.
Solution to Consecutive Integer Problem 13

14.
 Three consecutive integers are such that three times the smallest is 14 more than the largest.  Find the integers.
Solution to Consecutive Integer Problem 14
15.
 Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third.  Find the integers.
Solution to Consecutive Integer Problem 15
16.
 Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third.  Find the integers.
Solution to Consecutive Integer Problem 16
17.
 Two consecutive integers are such that 3 times the larger exceeds twice the smaller by 34.  Find the integers.
Solution to Consecutive Integer Problem 17

Answers:

  1.   61, 62

  2.  49, 48

  3.   56, 57, 58

  4.   19, 18, 17

  5.   26, 28

  6.   20, 18

  7.   26, 28, 30

  8.  18, 16, 14

  9.   63, 65

10.   19, 17

11.   23, 25, 27

12.   17, 15, 13

13.   33, 35, 37 14.    8, 9, 10 15.   21, 23, 25 16.   20, 22, 24 17.   31, 32

Back to  NUMBER PROBLEMS 

© Copyright 2016 Howard Sorkin  All rights reserved