Query 28

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course Mth 151

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: 

 X = -15

 

 

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): ok

 

 

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Self-critique Rating: 3

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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: 

r = 0

 

 

confidence rating #$&*: 3

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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): ok

 

 

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Self-critique Rating:

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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: 

 T = 7000

 

 

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): ok

 

 

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Self-critique Rating: 3

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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: 

 B = 2A / h - 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): ok

 

 

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Self-critique Rating: 3

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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 = 50

 

 

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.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 - .3 = 13.5

2x = 13.5  + .3 = 13.8

x = 13.8 / 2 = 6.9.

 

x - .3 = 6.9. 6.9-.3 = 6.6.

 

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): ok

 

 

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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: 

 X = 1

 

 

confidence rating #$&*: 3

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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): ok

 

 

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Self-critique Rating: 3

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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 nickels, 2 quarters, and 4 half-dollars

 

 

confidence rating #$&*: 3

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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.**

 

 

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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 nickels, 2 quarters, and 4 half-dollars

 

 

confidence rating #$&*: 3

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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.**

 

 

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Self-critique (if necessary):

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Self-critique rating:

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