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.
Your solution:
Confidence Assessment:
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.
Your solution:
Confidence Assessment:
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):
Self-critique Rating:
Question: `q7.1.45 .20 ( 14000) + .14 t = .18 (14000 + t ). Show how you solved the equation for t.
Your solution:
Confidence Assessment:
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
Your solution:
Confidence Assessment:
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):
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?
Your solution:
Confidence Assessment:
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.
Your solution:
Confidence Assessment:
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.
Your solution:
Confidence Assessment:
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):
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.
Your solution:
Confidence Assessment:
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.**