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# Consumer Mathematics

### Word Problem : Complete a table and write a rational expression involving rate.

Kent can Paint a certain house by himself in x days. His helper Keith can paint the same house by himself in x + 3 days. Suppose that they work together on the job for 2 days. To complete the table, use the fact that the work completed is the product of the rate and the time. Write a Rational expression for the fraction of th

### Ratio and Proportion Word Problem

If 300 of 560 voters surveyed said they would vote for the incumbent, how many votes could the incumbent expect out of 843,000 votes?

### Details of a Fraction Word Problem

Students with a class size of under 30,have finished their tests. One third of the class received a "B," one quarter a "B-",and one sixth a "C". One eighth of the class Failed. How many students in class received an A?

### Subtraction of polynomial fractions

Perform the indicated subtraction x/x^2-2x-3 - 3x/x^2-9

### Ratio and Proportion : Elk and Fuel Efficiency

1. Park rangers catch, tag, and then release 140 elk back into a national park. One month later, they select a sample of 130 elk, 91 of which are tagged. Assuming the ratio of tagged elk in the sample holds for all elk in the park, approximately how many elk are in the park? 2. The formula M = 0.0075x2 - 0.2676x + 14.8 mode

### Word Problems : System of Equations and Ratio and Proportion

An investor bought 2000 shares of stock. An initial purchase was for \$12 per share and a second purchase was for \$18 per share. If \$27,000 worth of stock was purchased, how many shares were purchased at each price? A saltwater solution is formed by mixing 3 lbs of salt with 15 gal of water. At this rate how many additiona

### Fraction Application Problem

The amount of the ingredients needed to make 3 and 5 servings of rice are: to make rice and water salt butter _________________________________________ 3 servings 1 cup 3/8 tsp 1 1/2 tsp 5 servings 1 2/3 cup 5/8 tsp 2 1/2 tsp Find the amount of each ingredient

### Earned the most money

1)Jack earned twice as much as Mary and Jill earned \$8 more than Mary. Who earned the most money? Explain why. 2)A tire dealer sells 2 tires for as much as he paid for 3 tires. He paid \$240 for a dozen tires. What is the total profit on 12 tires? (See attachment for other two questions)

### Understanding the Basics of Fractions

Explain how you would help students understand that 3/4 is the same as 0.75. Include in your development a translator to 75/100 and from that form to the decimal from using models fo each translation. Also, how would you teach students to compare the fractions 3/7 and 5/8 without using models or cross-multiplying to identify whi

### Financial Problem: Determining the Firm's Economic Order Quantity

Tool Mart sells 1400 electronic water pumps every year. These pumps cost \$54.30 each. If annual inventory carrying costs are 12% and the cost of placing an order is \$90, what is the firm's EOQ? (Q*= Sq root of 2(S)(D)/C)Also: (C = Inventory carrying cost X cost of frames)

### Financial Problem: Determining Interest Savings

Pronet has annual sales of \$724 million from its 600 retail stores. Pronet can reduce its mail float by 2 days through the use of wire transfers. The annual cost of the wire transfers is expected to be \$105,610. If Pronet's cost of short-term funds is 9.75 percent, should the change to wire transfers be made? Assume 365 days per

### Mathematical Modelling; Modelling Cycle

Consider the following situation: {see attachment} Develop a mathematical model which describes the contractors profit from the days work [a very simple model will do]. Then show how, using the modelling cycle, this model might be revised into a sequence of successively more sophisticated mathematical models, which show how the

### Applications of ratios and proportions

The Golden Ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than the width, then for what dimensions would the length and width have the golden ratio? Let x=

### Partial Fraction Sums

Express f(x) as the sum of partial fractions. f(x)=(3x^2+10x+9)/(2x^3+8x^2+10x+4) This is what I've done so far. f(x)= (3x^2+10x+9)/(2x^3+8x^2+10x+4) = (3x^2+10x+9)/((x+2)(2x+2)(x+1)) = (3x^2+10x+9)= a/(x+2)+b/(2x+2)+c/(x+1) Giving the simultaneous equations: 3=2a+b+2c 10=4a+3b+6c 9=2a+2b+4c

### Reducing polynomial fractions

Reduce each answer to the lowest terms (see attachment)

### Fraction Equation Shown

2m 3m ___ = _____ 3 2

### I need help with these problems, I will give examples for each one,,,,

For O.T.A 103997,,, Example 1,, find the LCD for the given rational expression, and convert into an equivalent rational expression with the LCD as the denominator, X Y 1 - - - 9y5z, 12x3, 6x2y Example 2,, find the LCD for the given rational expression, and convert this rational expression into an

### Lorenz Equations and Equilibrium

Please see the attached file for the fully formatted problems. Show that for , the equilibrium (x*, y*, z*) = (0, 0, 0) is globally (nonlinearly) stable for the Lorenz system. That is, any (x(t), y(t), z(t)) would eventually approach (0, 0, 0) as . Consider the "volume" (a) Show that, using the Lorenz equations

### Using Rectangles for Fraction Addition and Fraction Expression

A. Use a rectangle to explain the process of adding 1/4 and 2/3 - Explain your answer. B. What multiplication problems are represented by each of the following area models? What are the products? (The 1st area model looks like one big rectangle with fifteen little rectangles in it, and 8 of them are shaded) (The 2nd area mo

### Simplifying Fraction Denominators

Simplify attached fractions with polynomial denominators.

### Fractions : Word Problem

All of the primary students at the Sunshine Elementary School were present on the day that one-third of the class went on the science field trip. Two fifths of the remaining primary students went skating at the local rink.If there were 36 primary students remaining at school, how many primary students attend Sunshine Elementary?

### Multiplying fractions

11 /13 X 2/121

5/7 + 2/5 + 1/15 Add these

### Example Word Problem: Fractions

Mr. and Mrs. Samuel visited Florida and purchased 120 oranges. They gave 1/4 of them to relatives ate 1/12 of them in the hotel and gave 1/3 of them to friends. They shipped the rest home to Illinois. a. How many oranges did they ship? b. If it costs 24 cents for each orange to be shipped to Illinois, what was the total ship

5/x-3 + 2/x-2 - 6/x+1

### Ratio and Proportion: Cat-Mice Problem

Five cats can catch 5 mice in 5 minutes. At this rate, how many cats are needed to catch 100 mice in 100 minutes? (Hint: it is not 100.)

### Linear equations: Word problem. Bill owns a bike company, and wants to know how many bicycles and tricycles he should manufacture, with no leftovers, and how many boxes of seats he will order. (details given in actual problem)

Bill runs Bill's Big Bikes, a company that manufactures bicycles and specialty adult-sized tricycles. The bicycles and tricycles use the same-sized wheels and identical seats. Right now, Bill has 68 wheels in the shop and needs to order seats. Unfortunately, the company that supplies the seats will only ship seats in boxes of

### Equations with fractions

Solve for x: x/(x^2-4)+1/(x+2)=3

### Working with metric conversions: Drug dosage

A client has an order for a foot soak prepared with 25% povidine iodine and the total volume of preparation is to be 1 liter. How many mls of povidine/iodine should be used?

### Writing fractions with the same denominator

Write (x+4)/(x^2-3x-10) and 2x/(25-x^2) with the same denominator.