Algebra III Page 2

Linear Functions II

1. The maximum recommended slope of a wheelchair ramp is . A business is installing a wheelchair ramp that rises 22 inches over a horizontal length of 24 feet. Is the ramp steeper than recommended?

2. A kitchen appliance manufacturing company determines that the total cost in dollars of producing x units of a certain blender is . Describe the practical significance of the y-intercept and the slope of this line.

$3500 represents the cost of other items other than production parts.

3. The revenue per share for Ebay, Inc. was $0.20 in 1998 and $0.92 in 2001. Assuming linear growth, write an equation that gives the revenue per share in terms of the year. Predict the revenue per share for the year 2008.

$2.60

4. Your publishing company has purchased a $12,000 machine that has a useful life of 8 years. The salvage value at the end if the 8 years is $2,000. Write a linear equation that describes the book value of the machine each year.

5. In 1996, there were 3927 J.C. Penney stores and in 2000 there were 3800 stores. Write a linear equation that gives the number of stores in terms of the year. Predict the number of stores for the years 2005 and 2010.

6. A microchip manufacturer pays its assembly line workers a daily wage of $125. In addition, workers receive a piecework rate of $0.75 per unit produced. Write a linear equation for the daily wage W in terms of the number of units x produced.

7. A roofing contractor purchases a shingle delivery truck with a shingle elevator for $16,500. The vehicle requires an average expenditure of $5.25 per hour for fuel and maintenance and the operator is paid $11.50 per hour.

a) Write a linear equation giving the total cost C of operating this equipment for t hours. (Include the purchase cost of the equipment.)

b) Assuming the customers are charged $67 per hour of machine use, write an equation for the revenue R derived from h hours of use.

c) Use the profit formula to write an equation derived from h hours of use.

d) Use the result of part c to find the break-even point – that is the number of hours this equipment must be used to yield a profit of 0 dollars.

8. A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear.

a) Write the equation of the line giving the demand x in terms of the rent p.

b) Use this equation to predict the number of units occupied when the rent is $655.

c) Predict the number of units occupied when the rent is $595.

9. The length and width of a rectangular of a rectangular garden are 15 feet and 10 feet respectively. A walkway of width x surrounds the garden.

a) Write an equation for the perimeter y of the walkway in terms of x.

b) Determine the slope of the equation from part (a). For each additional one-foot increase in the width of the walkway, determine the increase in the perimeter.

10. A pharmaceutical salesperson receives a monthly salary of $2500 plus a 7% commission of sales.

a) Write a linear equation for the salesperson’s monthly wage W in terms of sales S.

b) What would this salesperson’s monthly salary be if he sold $400,000 worth of pharmaceuticals?

c) How much in monthly sales would have to be made to earn a monthly salary of $6000?

11. The cost C for making x cases of pet food is given by . Each case of 100 boxes sells for $120.

a) How many cases must be sold for the company to break even?

b) How many cases must be sold for the company to make $5,000?

Mr. John Cendrowski

Lower Moreland HS