Query 27

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course Mth 151

4/9 4:37

The r If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://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

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

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Your solution: 4(x-9) = 8(x+3)

4x-36 = 8x+24 First we multiply on each side.

-4x = 60 Then we simplify and switch sides with some of the numbers.

-4x/-4 = 60/-4 Divide each side by -4.

X = -20

confidence rating #$&*: 3

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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.**

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Self-critique (if necessary): Oh, I didn’t divide both sides by 4 at the beginning.

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Self-critique Rating:1

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

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Your solution: I’m scared to work this problem out. I think that I should multiply all of them by 21, but I want to look and see.

confidence rating #$&*: 1

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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. **

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Self-critique (if necessary): Okay. Yes I do multiply by 21. Good.

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Self-critique Rating:1

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

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Your solution: (14000)+ .14 t = .18(14000 + t)

(14000) + .14t = 2520 + .18t

11480 = .04t

287000 = t

confidence rating #$&*: 3

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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. **

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Self-critique (if necessary): I was missing part of the problem. I didn’t realize that the .20 was part of the problem because I assumed it was part of the numbers that tell which problem it is.

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Self-critique Rating: 0

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

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Your solution: Divide both sides by h. Now the h is eliminated. 1/2B + 1/2b

@&

When you divide both sides by h, the left-hand side becomes A / h. The right-hand side is as you say.

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A-1/2b = 1/2B

@&

This would be

A / h - 1/2 b = 1/2 B

(see my previous note).

You would then multiply both sides by 2, obtaining

2 * A / h - 2 * 1/2 b = B.

Simplifying:

B = 2 A / h - b.

*@

a-b=B

confidence rating #$&*: 3

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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. **

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Self-critique (if necessary): Whoa! I’m way off!

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Self-critique Rating:0

@&

Not that far off but you did miss a couple of steps. Check my notes.

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

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Your solution: x + (x+20) = 102

2x +20 = 102

2x = 102-20

2x=82

X= 41

41 million viewers watched on Saturday. 61 million viewers watched on Thursday. 41+61= 102.

confidence rating #$&*: 3

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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.

SELF CRITIQUE: The problem had the number 102 while the solution had 120.

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.

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Your solution: x + (x - .3) = 13.5

2x= 13.5+.3

2x = 13.8

X = 6.9

GM has 6.9 billion. GE has 6.6 billion.

confidence rating #$&*: 3

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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. **

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Self-critique (if necessary):

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Self-critique Rating:3

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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.

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Your solution: I don’t know how to figure this one out.

confidence rating #$&*: 0

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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. **

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Self-critique (if necessary):

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Self-critique Rating:0

@&

Mixture problems are pretty challenging. I remember in high school, a long time ago of course, when they drove me nuts for about a week.

What do you and do you not understand about the given solution?

*@

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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.

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Your solution: 2.6 = x.05 + (x.05+20) + 2(x.05(x.05 + 20))

2.6= 2x.05 + 20 + 4x.05 +40

2.6= 6x.05+60

2.6-60= 6x.05 +60-60

-57.4= 6x.05

confidence rating #$&*: Ummmm…. I don’t think I’m doing this right.

@&

Your notation might be confusing you. You seem to be on the right track.

I know what you mean by some of your notation, and it can be clarified pretty easily. An expression like x.05 can be a little confusing on your end; it looks a bit like a decimal number. .05 * x or just .05 x is more standard notation.

When you write x.05 + 20, for example, it's not clear what the 20 means. You probably intend x * .25, which can be written as .25 x. This would be the value of x quarters.

Your expression 2 ( x.05 ( x.05 + 20) ) is probably intended to represent the value of the half-dollars. There are 2 x half-dollars. The value of each is .5 dollars, so their value is 2x * .5, which is the same as .5 * 2 x, which in turn simplifies to give you just x.

*@

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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.**

atio of the areas is therefore 16 cm^2/(40,000 cm^2) = 1 / 25

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Self-critique (if necessary):

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Self-critique rating:

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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.

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Your solution: 2.6 = x.05 + (x.05+20) + 2(x.05(x.05 + 20))

2.6= 2x.05 + 20 + 4x.05 +40

2.6= 6x.05+60

2.6-60= 6x.05 +60-60

-57.4= 6x.05

confidence rating #$&*: Ummmm…. I don’t think I’m doing this right.

@&

Your notation might be confusing you. You seem to be on the right track.

I know what you mean by some of your notation, and it can be clarified pretty easily. An expression like x.05 can be a little confusing on your end; it looks a bit like a decimal number. .05 * x or just .05 x is more standard notation.

When you write x.05 + 20, for example, it's not clear what the 20 means. You probably intend x * .25, which can be written as .25 x. This would be the value of x quarters.

Your expression 2 ( x.05 ( x.05 + 20) ) is probably intended to represent the value of the half-dollars. There are 2 x half-dollars. The value of each is .5 dollars, so their value is 2x * .5, which is the same as .5 * 2 x, which in turn simplifies to give you just x.

*@

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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.**

atio of the areas is therefore 16 cm^2/(40,000 cm^2) = 1 / 25

"

Self-critique (if necessary):

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Self-critique rating:

#*&!

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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: 2.6 = x.05 + (x.05+20) + 2(x.05(x.05 + 20))

2.6= 2x.05 + 20 + 4x.05 +40

2.6= 6x.05+60

2.6-60= 6x.05 +60-60

-57.4= 6x.05

confidence rating #$&*: Ummmm…. I don’t think I’m doing this right.

@&

Your notation might be confusing you. You seem to be on the right track.

I know what you mean by some of your notation, and it can be clarified pretty easily. An expression like x.05 can be a little confusing on your end; it looks a bit like a decimal number. .05 * x or just .05 x is more standard notation.

When you write x.05 + 20, for example, it's not clear what the 20 means. You probably intend x * .25, which can be written as .25 x. This would be the value of x quarters.

Your expression 2 ( x.05 ( x.05 + 20) ) is probably intended to represent the value of the half-dollars. There are 2 x half-dollars. The value of each is .5 dollars, so their value is 2x * .5, which is the same as .5 * 2 x, which in turn simplifies to give you just x.

*@

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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.**

atio of the areas is therefore 16 cm^2/(40,000 cm^2) = 1 / 25

"

Self-critique (if necessary):

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Self-critique rating:

#*&!#*&!

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