#$&* course Mth 151 028. `query 28
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Given Solution: `a** Divide both sides by 4 to get x - 9 = 2(x+3). Then apply the Distributive Law to get x - 9 = 2 x + 6. Then add -x to both sides: x - 9 - x = 2 x + 6 - x. Simplify -9 = y + 6. Add -6 to both sides -9 - 6 = y + 6 - 6. Simplify -15 = x. The solution is x = -15.** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Ok. I did it differently but came up with the same solution. ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.1.39 (2r - 3 ) / 7 + 3/7 = -r/3. Show how you solved the equation for r. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: To get rid of the fractions, multiply all parts of the equation by 21 21 [(2r - 3 ) / 7] + 21(3/7) = 21(-r/3) 3(2r - 3) - 9 = -7r Distributive property to first part 6r - 9 - 9 = -7r 6r = -7r Subtract 13r = 0 Divide r = 0 confidence rating #$&*: OK ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.1.45 .20 ( 14000) + .14 t = .18 (14000 + t ). Show how you solved the equation for t. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: .20 (14000) + .14 t = .18 (14000 + t ) Distributive property 2800 + .14t = 2520 + .18t Subtract 280 + .14t = .18t Subtract decimals 280 = .040t Divide 7000 = t confidence rating #$&*: OK ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aCORRECT STUDENT SOLUTION WITH INSTRUCTOR COMMENT: .20(14,000)+.14t=.18(14,000+t) 2800+.14t=2520+.18t -.14t+2800+.14t=2520+.18t-.14t 2800=2520+.04t -2520+2800=2520+.04t-2520 280=.04t 280/.04=.04t/.04 7000=t INSTRUCTOR COMMENT: Correct solution but you're better off if you can avoid decimals and the attendant risk of misplacing one. One possible sequence of steps: First multiply both sides by 100 to avoid having to deal with decimals: 20 ( 14000) + 14 t = 18 ( 14000 + t). Divide both sides by the common factor 2: 10 ( 14000) + 7 t = 9 ( 14000 + t). Simplify: 140,000 + 7 t = 126,000 + 9 t. Add -9 to both sides: 140,000 + 7 t - 9 t = 126,000 + 9 t - 9 t. Simplify 140,000 - 2 t = 126,000. Add -140,000 to both sides: 140,000 - 2 t = 126,000 - 140,000. Simplify: -2 t = -14,000. Divide both sides by -2: t = 7000. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Ok and I understand how decimals can be more complicated ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.1.70 A = 1/2 ( B + b ) * h. Show how you solved the equation for B YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The goal here is to get B by itself The first thing is to get rid of the fraction so you multiply both sides by 2 2A = (B + b) * h Since the side with B is being multiplied by h, you do the opposite and divide 2A/h = (B + b) Since the side with B has b being added to it, you subtract it 2A/h - b = B confidence rating #$&*: 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* 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: Let x = Saturday viewers Let x + 20 = Thursday viewers x + (x + 20 ) = 120 2x + 20 = 120 2x = 100 x = 50 50 million = Saturday viewers 70 million = Thursday viewers confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** If we have 20 million more on Thursday then if x = number of Saturday viewers in millions, the number of Thursday viewers is x + 20, again in millions. The total number is 120 million so we have # of Thursday viewers + # of Saturday viewers = 120; using our expressions we have (x + 20) + x = 120 so that 2x + 20 = 120. Adding -20 to both sides we get 2x + 20 - 20 = 120 - 20 or 2x = 100. Dividing both sides by 2 we get (2x) / 2 = 100 / 2 so that x = 50. Thus the number of Saturday viewers is 50, representing 50 million, and the number of Thursday viewers is x + 20 = 70, representing 70 million.GE and GM total 13.5 billion; GE .3 billion less than GM. Show how you set up and solved an equation to obtain the profits of both companies. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Let x = GM Let x - .3 = GE x + (x-.3) = 13.5 x + x - .3 = 13.5 2x - .3 = 13.5 2x = 13.8 x = 6.9 GM = x = 6.9 billion GE = x - .3 = 6.6 billion confidence rating #$&*: 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* 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 ) .120 = .090 + .03x .030 = .03x 1 = x confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.2.50 Equal #'s of nickels and quarters, twice as many half-dollars; total $2.60. Show how you solved the problem by setting up and solving an equation. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Let x = nickels Let x = quarters Let 2x = half dollars .05x + .25x + .5 (2x) = 2.60 1.30x = 2.60 Divide x = 2 x = 2 = nickels x = 2 = quarters 2x = 4 = half dollars confidence rating #$&*: 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.** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q7.2.50 Equal #'s of nickels and quarters, twice as many half-dollars; total $2.60. Show how you solved the problem by setting up and solving an equation. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Let x = nickels Let x = quarters Let 2x = half dollars .05x + .25x + .5 (2x) = 2.60 1.30x = 2.60 Divide x = 2 x = 2 = nickels x = 2 = quarters 2x = 4 = half dollars confidence rating #$&*: 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.** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&! ********************************************* Question: `q7.2.50 Equal #'s of nickels and quarters, twice as many half-dollars; total $2.60. Show how you solved the problem by setting up and solving an equation. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Let x = nickels Let x = quarters Let 2x = half dollars .05x + .25x + .5 (2x) = 2.60 1.30x = 2.60 Divide x = 2 x = 2 = nickels x = 2 = quarters 2x = 4 = half dollars confidence rating #$&*: 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.** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!