Query 71 72

#$&*

course mth 151

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

028. `query 28

*********************************************

Question: `q7.1.18 4(x-9) = 8(x+3). Show how you solved the equation for x.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

4x-36/4=8x+24/4

x-9=2x+6/x-2x 2x+12-2x

x-9+9=2x+6+9

-x=15

x=-15

confidence rating #$&*: 2

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** Divide both sides by 4 to get

x - 9 = 2(x+3). Then apply the Distributive Law to get

x - 9 = 2 x + 6. Then add -x to both sides:

x - 9 - x = 2 x + 6 - x. Simplify

-9 = y + 6. Add -6 to both sides

-9 - 6 = y + 6 - 6. Simplify

-15 = x.

The solution is x = -15.**

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:

*********************************************

Question: `q7.1.39 (2r - 3 ) / 7 + 3/7 = -r/3. Show how you solved the equation for r.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(2r-3)/7+3/7=-r/3

21(2r-3)/7+21+3/7=r/3

@&

Your right-hand side should be 21 * r / 3.

You have to multiply the entire equation by the common denominator.

*@

42r-63/7

6r-9+24/7

6r-9+9=24/7+9/1

6r/6=12.43/6

r=2.07

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

2

.............................................

Given Solution:

`a** You don't want to deal with fractions so you do best to multiply both sides by the common denominator 21 to get

21 (2r - 3) / 7 + 21 * 3 / 7 = 21 * (-r/3), which simplifies to

3 (2r - 3) + 9 = -7 r. The expand on the left using the Distributive Law:

6 r - 9 + 9 = - 7 r. -9 + 9 = 0; add 7 r to both sides:

6 r + 7 r = 0 so

13 r = 0 and

r = 0 / 13 = 0. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):HELp... I messed this one up

------------------------------------------------

Self-critique Rating:

*********************************************

Question: `q7.1.45 .20 ( 14000) + .14 t = .18 (14000 + t ). Show how you solved the equation for t.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

.20(14000)=.14t=18(14000+t)

2800=.14t=2520+18t

18t-.14t=2800-2520

.04t/.04=280/.04

t=7000

confidence rating #$&*: 2

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`aCORRECT STUDENT SOLUTION WITH INSTRUCTOR COMMENT:

.20(14,000)+.14t=.18(14,000+t)

2800+.14t=2520+.18t

-.14t+2800+.14t=2520+.18t-.14t

2800=2520+.04t

-2520+2800=2520+.04t-2520

280=.04t

280/.04=.04t/.04

7000=t

INSTRUCTOR COMMENT:

Correct solution but you're better off if you can avoid decimals and the attendant risk of misplacing one.

One possible sequence of steps:

First multiply both sides by 100 to avoid having to deal with decimals:

20 ( 14000) + 14 t = 18 ( 14000 + t). Divide both sides by the common factor 2:

10 ( 14000) + 7 t = 9 ( 14000 + t). Simplify:

140,000 + 7 t = 126,000 + 9 t. Add -9 to both sides:

140,000 + 7 t - 9 t = 126,000 + 9 t - 9 t. Simplify

140,000 - 2 t = 126,000. Add -140,000 to both sides:

140,000 - 2 t = 126,000 - 140,000. Simplify:

-2 t = -14,000. Divide both sides by -2:

t = 7000. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:

*********************************************

Question: `q7.1.70 A = 1/2 ( B + b ) * h. Show how you solved the equation for B

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

1/2(B+b)*h

confidence rating #$&*: 1

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** You need to isolate B:

First multiply both sides by 2 and get

2A= (B+b) *h . Next divide both sides by h to get

2A / h = B + b. Then subtract b:

2A / h - b = B.

Thus B = 2A / h - b. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):HELP

@&

&#Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the parts of the given solution on which your solution didn't agree, and if necessary asking specific questions (to which I will respond).

&#

*@

------------------------------------------------

Self-critique Rating:

*********************************************

Question: `q7.2.18 20 million more viewers on Thursday than on Saturday; the total number is 102 million. How many watch each night?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

x+x+20=120

2x+20=120

2x+20-20=120-20

2x/2=100/2

x=50

5-+20=70

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** If we have 20 million more on Thursday then if x = number of Saturday viewers in millions, the number of Thursday viewers is x + 20, again in millions.

The total number is 120 million so we have

# of Thursday viewers + # of Saturday viewers = 120; using our expressions we have (x + 20) + x = 120 so that

2x + 20 = 120. Adding -20 to both sides we get

2x + 20 - 20 = 120 - 20 or

2x = 100. Dividing both sides by 2 we get

(2x) / 2 = 100 / 2 so that

x = 50.

Thus the number of Saturday viewers is 50, representing 50 million, and the number of Thursday viewers is x + 20 = 70, representing 70 million.GE and GM total 13.5 billion; GE .3 billion less than GM. Show how you set up and solved an equation to obtain the profits of both companies.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: see above

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** If GE makes .3 billion less than GM then if x = GM profits in billions we can say that the GE profits are x - .3. Thus we have

x + (x-.3) = 13.5. This gives us

2x - .3 = 13.5 so that

2x = 13.5 + .3 = 13.8 and

x = 13.8 / 2 = 6.9.

It follows that x - .3 = 6.9 so that x = 6.9-.3 = 6.6.

So GM profits are 6.9 billion and GE profits are 6.6 billion. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:

*********************************************

Question: `q7.2.40 Water added to 3 gal of 4% soln to get 3% soln. Show how you solved the problem by setting up and solving an equation.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

.04*3=.03 (3+x)

.12=.09+3x-.09

@&

.03 ( 3 + x) = .03 * 3 + .03 * x, by the distributive law.

.03 * 3 = .09, and .03 * x = .03 x.

You won't get 3 x.

*@

.12-.09=3x

.03=3x/3

.03/3.

.01=x

confidence rating #$&*: 2

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** You need to first specify what x is.

If x is the number of gallons of water added, then :

After adding 3 gallons we have 3 + x gallons of 3% solution.

Originally we had .04 * 3 gallons of the solute, and since we add only water that's what we still have after adding the water.

But now the solute is in 3+x gallons of solution and its concentration is 3%.

We have the same amount of solute after as before, since all we added was water, so

.04 * 3 = .03 * ( 3 + x ).

We solve this equation to get x, the number of gallons of water added. We obtain x = 1.

The number of gallons added will be exactly 1. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):Where did I go wrong with my numbers/decimal

------------------------------------------------

Self-critique Rating:

*********************************************

Question: `q7.2.50 Equal #'s of nickels and quarters, twice as many half-dollars; total $2.60. Show how you solved the problem by setting up and solving an equation.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

2x+x=2.60

3x/3=2.60/3

.87

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a**If x is the number of nickles then we have x quarters and 2x half-dollars. So the amount of money we have is

.05 x + .25 x + .5 (2x).

This amount is 2.60 so

.05 x + .25 x + .5 (2x) = 2.60. Simplifying the left-hand side:

.05 x + .25 x + x = 2.60

1.30 x = 2.60 so that

x = 2.60 / 1.30 = 2.

We have 2 nickles, 2 quarters and 4 half-dollars.**

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

*********************************************

Question: `q7.2.50 Equal #'s of nickels and quarters, twice as many half-dollars; total $2.60. Show how you solved the problem by setting up and solving an equation.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

2x+x=2.60

3x/3=2.60/3

.87

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a**If x is the number of nickles then we have x quarters and 2x half-dollars. So the amount of money we have is

.05 x + .25 x + .5 (2x).

This amount is 2.60 so

.05 x + .25 x + .5 (2x) = 2.60. Simplifying the left-hand side:

.05 x + .25 x + x = 2.60

1.30 x = 2.60 so that

x = 2.60 / 1.30 = 2.

We have 2 nickles, 2 quarters and 4 half-dollars.**

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

#*&!

&#Your work looks good. See my notes. Let me know if you have any questions. &#