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VII-8  SOLVE WORD PROBLEMS

 

 

Find 3 consecutive odd integers whose sum is 153.  Let x = the first odd integer.  The next odd integer would be that number (x) plus 2 and the 3rd odd number would be x + 2 + 2.  All 3 numbers added together would be 153, so we have the equation:

 

x + (x + 2) + (x +2 +2) = 153.  

Simplify the left

side

3x + 6                          = 153   

Subtract 6 from both sides

3x                             = 147  

Divide both sides by 3

x                           = 49

 

x + 2              = 51

next odd number is x + 2

x  + 2 +2 =    53             

next odd # is

 x + 2 + 2

 

 

Ex. 2. The length of a rectangle is 3 times its width.  If the area is 432 square meters, find the dimensions.

 let w =width  then length l = 3w

Formula for area of rectangle is A =  l w     

                

A = l w              

plug  values in                      

432 sq meters = (3w)(w)

 

432 sq meters = 3w2

divide both sides by 3

144 sq meters =  w2

take sq. rt.  both sides                   

12 meters  =   w

 

      and l = 3w or l = 3(12) = 36

 

EX. 3.   If a person earns a 6% commission on sales, find the amount of commission earned on a sale of $2150.00.

Amount of commission = rate (changed to decimal) times amount of sales.  

 Let A = amount of commission          6% = .06

(% to dec. Move dec. pt. 2 places left & drop the % sign.)

A = rate times amount of sales.

  A =  .06($2150.00)  =  $129

 

I am 5 years more than twice LeAnn’s age.   LeAnn is 2 years older than Mark.  Mark is 22.  Find my age.

Work backwards.    Mark is 22.   LeAnn is 22 + 2 or 24.  Now translate the 1st sentence.  Let R = my age     R = 5 + 2(LeAnn’s age)

                R = 5 + 2(24)

                R = 5 + 48   = 53 years old  ( In 2001)

 

 The following are from Practice AHSGE Tests from Jacksonville State University

 

1.  Find 2 consecutive odd integers whose sum is   

     – 64.

 

2.  Find 3 consecutive integers whose sum is

       306.

 

3.  The length of a rectangle is twice the width.  If the area is 392 square feet, find the dimensions.

 

4.  If a person earns a 3% commission on sales, find the amount of commission earned on a sale of $4250.

 

5.  Robby earns $8.50 an hour and is paid time and a half for overtime.  Find his overtime rate.

 

6.  A dress that regularly sells for $60 is 25% off.  What is the amount of discount?

 

7.  A shirt that regularly sells for $31 is 25% off.  What is the sales price to the nearest cent?

 

8.  Byron buys a shirt that costs $24, jeans that cost $31, and belt that costs $12.  The sales tax is 8.5%.   Find the total price of the purchase including tax.

 

9.  Miranda is 4 years older than her sister Ashley.  The sum of their ages is 50.  How old is Ashley?

 

10.  Given the difference of 2 numbers is 42 and the sum of the numbers is 94, find the numbers

 

11.  A bank contains $2.60 in nickels and dimes.  There are 2 more dimes than nickels.  Find the number of dimes in the bank.

A.  16             B.   5           C.   10                D.   18

 

12.  John studied for 75 minutes.  How many hours did he study?

 

13.   Camilla traveled 420 miles at a rate of 70 miles per hour.  How long did she travel?

 

14.  Billy’s gross pay was $375.  He had the following deductions:  $24.59;  $110.41; and $53.50.  What was his net pay?

 

15.  How much money do you save by buying a 6-pack of soft drinks for $1.99 instead of buying 6 soft drinks for $.55 each?