Assignment 28

course Mth 151

????C??y????????assignment #028

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?w?????}??yO?????Liberal Arts Mathematics I

07-27-2006

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10:33:12

7.1.18 4(x-9) = 8(x+3). Show how you solved the equation for x.

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RESPONSE -->

4(x-9) = 8(x+3)

4x - 36 = 8x + 24

+36

4x = 8x + 60

-8x

-4x = 60

/-4

x = -15

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10:33:43

** 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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10:35:56

7.1.39 (2r - 3 ) / 7 + 3/7 = -r/3. Show how you solved the equation for r.

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RESPONSE -->

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

*21

3(2r - 3) + 9 = -7r

6r - 9 + 9 = -7r

6r = -7r

+7r

13r = 0

/13

r = 0

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10:36:11

** 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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10:39:24

7.1.45 .20 ( 14000) + .14 t = .18 (14000 + t ). Show how you solved the equation for t.

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RESPONSE -->

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

*100 to get rid of decimals

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

280,000 + 14t = 252,000 + 18t

-280,000

14t = -28,000 + 18t

-18t

-4t = -28,000

/-4

t = 7000

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10:40:01

CORRECT 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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10:43:53

7.1.70 A = 1/2 ( B + b ) * h. Show how you solved the equation for B

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RESPONSE -->

This one was a little more difficult for me. Here is what I have so far...

A = 1/2 (B+b)h

/ by 1/2

A/2 = (B+b)h

use distributive pro.

A/2 = Bh + bh

That's about as far as I got.

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10:45:23

** 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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RESPONSE -->

That was much easier than I thought. I messed my problem up big time. I think my first wrong step was the fraction. Fractions are not my favorite and I did'nt properly get rid of it.

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10:47:07

7.2.18 20 million more viewers on Thursday than on Saturday; the total number is 102 million. How many watch each night?

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RESPONSE -->

x + 20 = Thursday night

x = Saturday

x + x + 20 = 102

2x + 20 = 102

2x = 82

x = 41

Saturday = 41

Thursday = 61

total = 102

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10:47:53

** 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.

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10:53:13

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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RESPONSE -->

GE & GM = 13.5 billion

GE = x - .3

GM = x

x + x - .3 = 13.5

2x - .3 = 13.5

2x = 13.8

x = 6.9

GE = x - .3 = 6.6 billion

GM = x = 6.9 billion

total 6.6 + 6.9 = 13.5 billion

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10:53:27

** 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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10:58:01

7.2.40 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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RESPONSE -->

These word problems with % and tables kindof confuse me. Here is where I got stuck.

4% 3gallons 3(.04)

3% x .03x

The problem could be approached this way.

If x is the amount of 3% solution, then

3 * .04 = .03 x, which you easily solve to get

x = 4.

x - 3 gallons is the amount of water added, and you would get 4 - 3 = 1 gallon.

However be sure you also understand the given solution, in which x is the amount of water added.

I am not sure this is right and even if it is I am not sure what the next step would be or how to put it into an equation.

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11:00:29

** 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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RESPONSE -->

I understand when I read your comments, but I don't think that I can think of that on my own. I guess just working more problems will help me get the hang of it.

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11:09:29

7.2.50 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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RESPONSE -->

nickels = x

quarters = x

half-dollars = 2x

x .05 .05x

x .25 .25x

2x .50 (.5)2x

.05x + .25x + (.5)2x = 2.60

.05x + .25x + 1x = 2.60

1.30x = 2.60

x = 2

nickels = x = 2 = $.10

quarters = x = 2 = $.50

half-dollars = 2x = 4 = $2

total = 2.60

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11:09:45

**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.**

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11:09:45

**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.**

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Assignment 28

You're not doing badly here. Practice is the key on 'word problems'. See my note(s) and let me know if you have additional questions.

You're not doing badly here. Practice is the key on 'word problems'.

See my note(s) and let me know if you have additional questions.