SolutionGuideforPrologue:

Complete Solutions Manual

Functions & Change

A Modeling Approach to College Algebra

FIFTH EDITION

Bruce Crauder Oklahoma State University

Benny Evans Oklahoma State University

Alan Noell Oklahoma State University

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SolutionGuideforPrologue:

CalculatorArithmetic

CALCULATOR ARITHMETIC

1.Valentine's Day: To nd the percentage we rst calculate

Average female expenditure Average male expenditure =

$72:28

$129:95

= 0:5562:

Thus the average female expenditure was 55.62% of the average male expenditure.

2.Cat owners: First we nd the number of households that owned at least one cat. Be- cause 33% of the 116 million households owned at least one cat, this number is 33%116 = 0:33116 = 38:28million.Now 56% of those households owned at least two cats, so the number owning at least two cats is 56%38:28 = 0:5638:28 = 21:44million.Therefore, the number of households that owned at least two cats is 21.44 million.

3.A billion dollars: A stack of a billion one-dollar bills would be0:00431;000;000;000 = 4;300;000inches high. In miles this height is 4;300;000inches 1foot 12inches

1mile 5280feet = 67:87miles: So the stack would be 67.87 miles high.

4.National debt: Each American owed

$12;367;728million 308million

= $40;154:96or about 40

thousand dollars.

5.10% discount and 10% tax: The sales price is 10% off of the original price of $75.00, so the sales price is75:000:1075:00 = 67:50dollars. Adding in the sales tax of 10% on this sales price, we'll need to pay67:50 + 0:1067:50 = 74:25dollars.

6.A good investment: The total value of your investment today is: Original investment+13% increase= 850 + 0:13850 = $960:50: 2 / 4

• Solution Guide for Prologue

7.A bad investment: The total value of your investment today is: Original investment7% loss= 7200:07720 = $669:60:

8.An uncertain investment: At the end of the rst year the investment was worth

Original investment+12% increase= 1300 + 0:121300 = $1456: Since we lost money the second year, our investment at the end of the second year was worth Value at end of rst year12% loss= 14560:121456 = $1281:28: Consequently we have lost $18.72 of our original investment.

9.Pay raise: The percent pay raise is obtained from

Amount of raise Original hourly pay

:

The raise was9:509:25 = 0:25dollar while the original hourly pay is $9.25, so the fraction is

0:25

9:25

= 0:0270. Thus we have received a raise of 2.70%.

10.Heart disease: The percent decrease is obtained from

Amount of decrease Original amount

:

Since the number of deaths decreased from 235 to 221, the amount of decrease is 14 and so the fraction is 14 235

= 0:0596. The percent decrease due to heart disease is 5.96%.

11.Trade discount:

(a) The cost price is9:9940%9:99 = 5:99dollars.(b) The difference between the suggested retail price and the cost price is65:00 37:00 = 28:00dollars. We want to determine what percentage of $65 this difference

represents. We nd the percentage by division:

28:00

65:00

= 0:4308or43:08%. This is the trade discount used.

12.Series discount:

(a) Applying the rst discount gives a price of80:0025%80:00 = 60:00dollars.Applying the second discount to this gives60:0010%60:00 = 54:00dollars.The retailer's cost price is $54. 3 / 4

Calculator Arithmetic 3 (b) Applying the rst discount gives a price of100:0035%100:00 = 65:00dollars.Applying the second discount to this gives a price of65:0010%65:00 = 58:50 dollars. Applying the third discount gives58:505%58:50 = 55:575. The retailer's cost price is $55.58.(c) Examining the calculations in Part (b), we see that the actual discount resulting from this series is10055:575 = 44:425. This represents a single discount of about

44:43%off of the original retail price of $100.

(d) Again, we examine the calculations in Part (b). In the rst step we subtracted35%

of100from100. This is the same as computing65%of100, so it is1000:65. In

the second step we took10%of that result and subtracted it from that result; this is the same as multiplying1000:65by90%, or0:90, so the result of the second step is1000:650:90. Continuing in this way, we see that the result of the third step is1000:650:900:95. Here the factor0:65indicates that after the rst discount the price is65%of retail, the factor0:90indicates that after the second discount the price is90%of the previous price, and so on.

13.Present value: We are given that the future value is $5000 and thatr= 0:12. Thus the present value is Future value

• +r

= 5000

1 + 0:12

= 4464:29dollars:

14.Future value:

(a) A future value interest factor of 2 will make an investment double since an invest- ment ofPdollars yields a return ofP2or2Pdollars. A future value interest factor of 3 will make an investment triple.(b) The future value interest factor for a 7 year investment earning 9% interest com- pounded annually is (1 +interest rate) years

= (1 + 0:09)

7

= 1:83:

(c) The 7 year future value for a $5000 investment is Investmentfuture value interest factor= 50001:83 = $9150: Note: If the answer in Part (b) is not rounded, one gets $9140.20, which is more accurate. Since the exercise asked you to ”use the results from Part (b)...” and we normally round to two decimal places, $9150 is a reasonable answer. This illustrates the effect of rounding and that care must be taken regarding rounding of intermediate-step calculations.

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