College Algebra Tutorial 16


College Algebra
Answer/Discussion to Practice Problems  
Tutorial 16: Formulas and Applications


WTAMU > Virtual Math Lab > College Algebra > Tutorial 16: Formulas and Applications


 

 

check markAnswer/Discussion to 1a

In last night’s basketball game, Sally scored 9 less than twice what Lucy scored.  The sum of their scores is 27.  How many points did Sally and Lucy make individually?


 
Step 1: Understand the problem.

 
Make sure that you read the question carefully several times. 

We are looking for two numbers, and since we can write the number of points Sally made in terms of the number of points Lucy scored we will let 

x = the number of points Lucy scored

 

Sally scored 9 less than twice what Lucy scored:

2x - 9 = number of points Sally scored


 
Step 2:  Devise a plan (translate).

 
ad1a2

 
Step 3:  Carry out the plan (solve).

 
ad1a3
*Combine like terms

*Inv. of sub. 9 is add. 9

*Inv. of mult. by 3 is div. by 3

 


 
Step 4:  Look back (check and interpret).

 
If we add 12 and a 15 (a number 9 less than twice 12) we do get 27.
 
 

FINAL ANSWER:

The number of points Lucy scored was 12.

The number of points Sally scored was 15.


 
(return to problem 1a)


 

 

check markAnswer/Discussion to 1b

The heights in inches of three basketball players are 3 consecutive integers.  If the sum of twice the 1st, 3 times the 2nd, and the 3rd is 437, what are the three heights.


 
Step 1: Understand the problem.

 
Make sure that you read the question carefully several times. 

We are looking for 3 consecutive integers, we will let

x = 1st consecutive integer

x + 1 = 2nd consecutive integer

x + 2  = 3rd  consecutive integer


 
Step 2:  Devise a plan (translate).

 
ad1b1

 
Step 3:  Carry out the plan (solve).

 
ada1b2

*Remove ( ) by using dist. prop.
*Combine like terms

*Inv. of add. 5 is sub. 5
 

*Inv. of mult. by 6 is div. by 6

 


 
Step 4:  Look back (check and interpret).

 
If we take the sum of twice 72, three times 73, and 74, we do get 437
 
 

FINAL ANSWER:

The heights of the three basketball players in inches are 72, 73, and 74.


 
(return to problem 1b)


 

check markAnswer/Discussion to 1c

A rectangular floor has a perimeter of 54 feet.  If the length is 3 more than the width, what are the dimensions of the floor?


 
Step 1: Understand the problem.

 
Make sure that you read the question carefully several times. 
 

We are looking for the length and width of the rectangle.  Since length can be written in terms of width, we will let

w = width

 

length is 3 feet more than  the width:

w + 3 = length


 
Step 2:  Devise a plan (translate).

 
ad1c1

 
Step 3:  Carry out the plan (solve).

 
ad1c2b

*Remove ( ) by using dist. prop.
*Combine like terms

*Inv. of sub. 6 is add. 6

*Inv. of mult. by 4 is div. by 4
 

 


 
Step 4:  Look back (check and interpret).

 
If width is 12, then length, which is 3 feet more than the width, would have to be 15.  The perimeter of a rectangle with width of 12 feet and length of 15 feet does come out to be 54.
 

FINAL ANSWER:

Width is 12 feet.

Length is 15 feet.


 
(return to problem 1c)


 

 

check markAnswer/Discussion to 1d

The original price of a CD player was marked down 15% and is now $127.50, how much was the original price?


 
Step 1: Understand the problem.

 
Make sure that you read the question carefully several times. 

We are looking for the price of the CD player before the markdown, we will let

x = price of the CD player before the markdown. 


 
Step 2:  Devise a plan (translate).

 
ad1d1

 
Step 3:  Carry out the plan (solve).

 
ad1d2

*Combine like terms

*Inv of mult. .85 is div. by .85

 


 
Step 4:  Look back (check and interpret).

 
If you markdown 15% from $150 you would get $127.50.
 
 

FINAL ANSWER:

The original price is $150.

 
(return to problem 1d)

 


 

 

check markAnswer/Discussion to 2a

problem 2a for T


 
In this problem, we need to solve for T.  This means we need to get T on one side and EVERYTHING ELSE on the other side using inverse operations.

Let’s solve this formula for T:


 
ad2a

*Inverse of mult. by R is div. by R
 
 
 

*Formula solved for T
 


 
(return to problem 2a)


 

 

check markAnswer/Discussion to 2b

problem 2b for m


 
In this problem, we need to solve for m.  This means we need to get m on one side and EVERYTHING ELSE on the other side using inverse operations.

Let’s solve this formula for m:


 
ad2b

*Inverse of add. by D is sub. by D

*Inverse of mult. by p is div. by p
 
 

*Formula solved for m
 


 
(return to problem 2b)

 

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WTAMU > Virtual Math Lab > College Algebra > Tutorial 16: Formulas and Applications


Last revised on Dec. 15, 2009 by Kim Seward.
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