# Several algebra Word problems

Question 1

Dental services. The national cost C in billions of dollars for dental services can be modeled by the linear equation

C = 2.85n +30.52,

Where n is the number of years since 1990 (Health Care Financing Administration, www.hcfa.gov).

a) Find and interpret the C-intercept for the line.

b) Find and interpret the n-intercept for the line.

c) Graph the line for n ranging from 0 through 20

d) If this trend continues, then in what year will the cost of dental services reach 100 billion?

Question 2

64. Retirement pay. The annual Social Security benefit of a retiree depends on the age at the time of retirement. The accompanying graph gives the annual benefit for persons retiring at ages 62 through 70 in the year 2005 or later (Social Security Administration, www.ssa.gov). What is the annual benefit for a person who retires at age 64? At what retirement age does a person receive an annual benefit of$11,600? Find the slope of each line segment on the graph, and interpret your results. Why do people who postpone retirement until 70 years of age get the highest benefit?

(Retirement age, Annual Social Security benefit (dollars))

(62, 7000)

(64, 8000)

(67, 10,000)

(70, 12,400)

Question 3

80. Direct deposit. The percentage of workers receiving direct deposit of their paychecks went from 32% in 1994 to 60% in 2004 (www.directdeposit.com). Let 1994 be year 0 and

2004 be year 10.

a) Write the equation of the line through (0, 32) and (10, 60) to model the growth of direct deposit.

b) Use the accompanying graph to predict the year in which 100% of all workers will receive direct deposit of their paychecks.

c) Use the equation from part (a) to predict the year in which 100% of all workers will receive direct deposit

Question 4

Graph each inequality

2x<3y+6

Graph must be in excel format with shade.

Question 5

Bonus and taxes. A company has an income of $100,000 before paying taxes and a bonus. The bonus B is to be 20% of the income after deducting income taxes T but before deducting the bonus. So

B =0.20(100,000 -T ).

Because the bonus is a deductible expense, the amount of income tax T at a 40% rate is 40% of the income after deducting the bonus. So

T = 0.40(100,000 - B).

a) Use the accompanying graph to estimate the values of T and B that satisfy both equations.

b) Solve the system algebraically to find the bonus and the amount of tax.

Question 6

Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25.

What was the price of a book and what was the price of a magazine?

#### Solution Summary

A step by step solution is provided to all the problems.