MATH 3295 Lecture 9: The Paycheck Problem:Visualizing Equivalent Fractions

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scarletgrasshopper506

6 Oct 2017

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She then spends 3/5 of what remains on her house payment. She spends 1/3 of what is then left on other bills. Finally, she spends 1/4 of the remaining money for entertainment. This activity leaves her with , that she puts into savings. X*(1/6)=(1/6)x (x-1/6x)*(3/5)=x/2 (x-(x/6)-(x/2))*(1/3)=(x/9) (x-(x/6)-(x/2)-(x/9))*(1/4)=1/18x x-(x/6)-(x/2)-(x/9)-(x/18)=150 (18-3-9-2-1)x/18=150 x/6=150 x=900 so the salary is equal to . House- 3/5 of what is left of the 50/60 = 30/50. Bills 1/3 of what is left of 30/50=6 1/3. When working with fractions, you may have been told that you can create equivalent fractions by multiplying the numerator and denominator of a fraction by the same non-zero value. For example, (cid:2871)(cid:2872) can be rewritten as an equivalent fraction by multiplying the numerator and denominator both by 3 (i. e. , (cid:2871)(cid:2872) (cid:2871)(cid:2871)), resulting in 9(cid:2869)(cid:2870). Although this can be rationalized symbolically, (e. g. , (cid:2871)(cid:2871) is equivalent to 1, and multiplying (cid:2871)(cid:2872) by 1 won"t change the value of (cid:2871)(cid:2872) since (cid:2871)(cid:2872)(cid:2871)(cid:2871) (cid:2871)(cid:2871)

Related Questions

1. Evaluate the expression 2x - 2 for the value of x = -3

2. Factor: xsquare + 4x - 32 (x-4)(x+8) (x-4)(x-8) (x-4)(x-8) (x-16)

3. Factor: xsquare - 25 (x-5) (x+5)2 (x+5)(x-5) (x-5)(x-5)

4. Evaluate -u2v3 when u=4 and v=-2 128 64 32 -128

5. Using an online calculator, determine whether the value of x=7 is a solution of the equation. x Yes No

6. Explain why x=7 IS or IS NOT a solution of the equation. 7 + 1/x+2=8

7. Solve the equation and check your solution: -2 - 4x = 30

8. Solve the equation and check your solution: 67x - 24 = 3x + 8(8x - 3) 67 -3 -67 All real numbers

9. Solve the equation and check your solution. 5x/2 - x/6 = 14 10 6 7 9

10. Solve the quadratic equation by factoring: xsquare - 6x + 5 = 0 -1, 5 -1,-5 1,-5 1,5

11. The imaginary number i represents:

12. Find real numbers a and b such that the equation is true: a+ bi = 14 + 2i a=16, b=4 a=18, b=6 a=14, b=2 a=15, b=14

13. Find all solutions to the following equation. /4x - 8 = /4x + 9 x = -17/4 x=9 No solution x=-17

14. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for Jamesâ miles.

15. Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz. 10h - .25=450 10h + .25(10h)=450 h -.25 (10h)=450 10h - .25(10h)=450

16. Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work. 17. The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width. Hint: Perimeter = width + length + width + length

18. Twice a number is added to the number and the answer is 80. Write an equation to solve this problem. 2n + n=80 2n = 80 2n + 80=n 80 + n=2n

19. If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20. Multiply the following binomials: (x + 5)(x - 5)

Suppose that the daily cost, in dollars, of producing xtelevisions is

C(x) = 0.003x3 + 0.1x2 + 62x + 620

and currently 60 televisions are produced daily.

Use C(60) and the marginal cost to estimate the daily cost ofincreasing production to 63 televisions daily.

Round to the nearest dollar.

A) $5673
B) $5667
C) $5481
D) $5635

A company estimates that the daily revenue (in dollars) from thesale of x cookies is given by:

R(x) = 885 + 0.02x + 0.0003x²

Currently, the company sells 900cookies per day.

Use marginal revenue to estimatethe increase in revenue if the company increases sales by onecookie per day.

A) $0.56
B) $56.00
C) $0.92
D) $92.00

For the total-cost function

C(x) = 0.01x2 + 0.8x + 50

find ?C and C'(x) when x = 50 and ?x = 1

A) ?C = $1.00; C'(50) = $1.00
B) ?C = $1.81; C'(50) = $1.80
C) ?C = $1.81; C'(50) = $1.30
D) ?C = $1.81; C'(50) = $1.00

A company finds that when it spends x million dollars onadvertising, its profit P, in thousands of dollars, is given by

P(x) = 970 + 15x - 4x²

Currently the company spends 17 million dollars onadvertising.

Use the marginal profit to estimate the change in profit if thecompany increases its advertising expenditure by one milliondollars.

A) 255 thousand dollars
B) 119 thousand dollars
C) -121 thousand dollars
D) 970 thousand dollars

The total cost, in dollars, to produce x DVD players is C(x) =70 + 7x - x² + 2x³

Find the marginal cost when x = 3

A) $136
B) $66
C) $55
D) $125

Suppose that the weekly profit, in dollars, of producing andselling x cars is

P(x) = 0.006x³ - 0.3x² + 960x - 900

and currently 60 cars are produced and sold weekly.

Use P( 60) and the marginal profit when to estimate the weeklyprofit of producing and selling 61 cars.

Round to the nearest dollar.

A) $55,269
B) $56,083
C) $55,182
D) $55,183

A grocery store estimates that the weekly profit (in dollars)from the production and sale of x cases of soup is given by

P(x) = -5600 + 9.5x - 0.0017x²

and currently 1300 cases areproduced and sold per week.

Use the marginal profit toestimate the increase in profit if the store prodcues and sells oneadditional case of soup per week.

A) $7.29
B) $3877.00
C) $5.08
D) $5.52

The weekly profit, in dollars, from the production and sale of xbicycles is given by

P(x) = 40.00x - 0.005x²

Currently, the company producesand sells 800 bicycles per week.

Use the marginal profit toestimate the change in profit if the company produces and sells onemore bicycle per week.

A) 48.00 dollars
B) 32.00 dollars
C) 40.00 dollars
D) 20.00 dollars

A company estimates that the daily cost (in dollars) ofproducing x chocolate bars is given by

C(x) = 1635 + 0.02x + 0.0004x²

Currently, the company produces600 chocolate bars per day.

Use marginal cost to estimate theincrease in the daily cost if one additional chocolate bar isproduced per day.

A) $0.62
B) $0.50
C) $62.00
D) $50.00

10.

The profit, in dollars, from the sale of x compact disc playersis P(x) = x3 -8x2 + 9x + 7

Find the marginal profit when x = 10.

A) $149
B) $297
C) $290
D) $156

Dr. Jones has found that, over the years, 95% of the babies she has delivered weighed x pounds, where x-8.2]- 1.5 s0. " (SLO #2) 1. Solve the inequality. Show your work. 2. Interpret the meaning of your answer to part (a) in the context of this problem. 3. How likely (or unlikely) would it be for the next baby Dr. Jones delivers to weigh 6 pounds 5 ounces? Explain. Jennifer has a taco stand. She has found that her daily costs can be modeled by C(x)x2-40x + LO 610, where C(x) is the cost, in dollars, to sell x units of tacos. #1,6) (S 4. If she wants to keep her daily costs at $300, how many units of tacos does she need to sell? Give all possible answers, rounding off to nearest whole number. Show your work. 5. Which answer to part (a) makes the most sense from Jennifer's point of view? Explain why One model for the ideal body weight, W, for men (in kilograms) is W = 50 + 2.3(-60), where h represents height (in inches). ll. (SLO #5) 6. According to this model, what is the ideal weight of a 6-foot male? Do not round your answer. 7. Rewrite the function in order to express height as a function of weight. Call this function h. Show your work 8. Verify that the given function and your function from part (b) are inverses, by showing that (Wãh)(W) = W and that (hÂ» W)(h) = h. What is the height of a male whose ideal weight is 83 kg? Round to nearest inch. II. An independent home builder's annual profit, in thousands of dollars, can be modeled by the function 9. P(x) 5-152x3-143x2 + 1102x-1673, where x is the number of houses built in a year. His company can build at most 13 houses in a year. (SLO #1, 2, 6) 10. Find the y-intercept and explain what it means in this context. 11. Find the x-intercept(s) and explain what they mean in this context 12. Determine the domain of the function in the context of this problem. 13. How many houses should the builder construct in order to have a profit of at least $400,000? 14. How many houses should the builder construct in order to maximize profit? . The graph below represents the population of insects, in thousands, over a 12 month period beginning in March 2010. Use the graph to answer the questions. (SLO #3, 6) plm) 400 200 100 1234567 9 10 I 100 Months 15. Explain why an exponential or logarithmic function would not be used to model this graph. 16. What is the minimum possible degree polynomial that can model this graph? Explain 17. Find the x-intercept(s) and interpret their meaning in this context.

MATH 3295 Lecture 9: The Paycheck Problem:Visualizing Equivalent Fractions

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