Question

a company had a total debt of $320,000 in 1980. between 1980 and 1987 it was able to reduce its debt 15% each year. approximate the companys debt in 1987 to the nearest 1000

Answer 1

all right

Answer 2

begin with 320,000.

Answer 3

so in 1981 the debt would have been reduced by 15%....so 85% remains

Answer 4

rite

Answer 5

let's say X0 represents the debt in 1980

Answer 6

X1 is debt in 1981. debt in 1981 = debt in 1980 reduced by 15% which is just 85% of debt in 1980 --> X1 = (X0)*.85

Answer 7

oh my you lost me

Answer 8

all right

Answer 9

so, what would be the debt in 1981?

Answer 10

i was just having variables stand in for the amounts

Answer 11

would it be the same as 1980?

Answer 12

the company reduces its debt by 15% each year

Answer 13

so minus 15% each year?

Answer 14

so it'd be less than the year before

Answer 15

right, -15% per year

Answer 16

but another way to consider this would be that 85% of the amount remains from before

Answer 17

37999.85

Answer 18

is that the answer?

Answer 19

as the final answer? or just what would be the total debt in 1981?

Answer 20

total debt in 1981

Answer 21

no, how did you get that?

Answer 22

i minused 15% the debt from 1980

Answer 23

what value did you obtain for 15% of 320,000?

Answer 24

319,999.85

Answer 25

15% of 320,00 would be: 320,000*.15 = 48,000

Answer 26

320,000 - 48,000 = debt in 1981

Answer 27

why multiply?

Answer 28

where did you get 48,000??

Answer 29

.15 * 320,000

Answer 30

you lost me. im sorry im horrible at math

Answer 31

you need to determine what 15% of the debt in 1980 is. the value if $320,000

Answer 32

are you familiar with percentages?

Answer 33

yes

Answer 34

cool, so in this case, you need to first determine what 15% of 320,000.

Answer 35

thats how you got 48,000?

Answer 36

yeah. 15% is actually the decimal .15

Answer 37

i know

Answer 38

yeah, cool, so you just multiply the decimal form with the debt

Answer 39

so debt in 1981 would be debt in 1980 - 15% of the debt in 1980

Answer 40

so it would be 15% minus 7 years?

Answer 41

not quite

Answer 42

so here, I want to type out a general plan for how to solve this then step through it with you

Answer 43

ugh. okay so i would minus .15 every year with each new debt?

Answer 44

right

Answer 45

debt in 1981 = debt in 1980 - (.15 * debt in 1980)
debt in 1982 = debt in 1981 - (.15 * debt in 1981)
debt in 1983 = debt in 1982 - (.15 * debt in 1982)
debt in 1984 = debt in 1983 - (.15 * debt in 1983)
debt in 1985 = debt in 1984 - (.15 * debt in 1984)
debt in 1986 = debt in 1985 - (.15 * debt in 1985)
debt in 1987 = debt in 1986 - (.15 * debt in 1986)

Answer 46

or

debt in 1981 = debt in 1980 * .85

Answer 47

okay i dont want to do it that way the .85

Answer 48

its confusing

Answer 49

all right, that would give you less work however...less multiplying and subtracting ;)

Answer 50

but that is the general set up

Answer 51

i rather the long way so i dont get lost in the middle,

Answer 52

sure, no problem

Answer 53

yeah once you get it that way, i bet you can find the simpler way

Answer 54

so we did 1981?

Answer 55

do you think you can try to solve it?

Answer 56

yes

Answer 57

cool, i'll check it for you if you'd like

Answer 58

oh please give me 10min.

Answer 59

sure

Answer 60

okay i lost myself.

Answer 61

heh, just concentrate on find the debt of one year at a time

Answer 62

so how far did you get?

Answer 63

ok. we can step through this. what is the debt in 1980: 320,000. what is the debt in 1981?

Answer 64

i did and it keeps going down to 47999 and only going down after the decimal

Answer 65

we said 480000 before

Answer 66

we said that 48,000 was 15% of 320,000. 48,000 would be the amount that the debt was reduced BY. therefore. 320,000 - 48,000 is the debt in 1981

Answer 67

that would be 272000

Answer 68

correct

Answer 69

ok, so that is debt in 1981. we have debt in 1980 was 320,000. debt in 1981 was 272,000. now, what would be the debt in 1982?

Answer 70

no

Answer 71

heh, what's up?

Answer 72

you wold minus .15 from 272000??

Answer 73

to determine the debt in 1982. we would take the debt from 1981 (which we found is 272,000 ). so, i think what you're saying is right. find 15% of 272,000. then subtract that amount from 272,000 to find the debt in 1982

Answer 74

thats what i meant

Answer 75

cool, then you got it

Answer 76

i got 271999.85

Answer 77

so debt in 1982 is 272,000 - (15% * 272,000)...drum roll, which is?

Answer 78

you simply subtracted .15 from 272,000

Answer 79

you need to multiply then subtract

Answer 80

ugh okay

Answer 81

when i multiply i get 40800

Answer 82

ok. now subtract that from 272,000

Answer 83

272,000 - 40,800 is the debt in 1982

Answer 84

231200

Answer 85

ok so now for 1983

Answer 86

multiply 231200 * .15

Answer 87

nice
then subtract

Answer 88

196520

Answer 89

solid, and repeat for 1984...

Answer 90

seems like you got It, right?

Answer 91

1984 is 225998

Answer 92

yes

Answer 93

hey, sorry, did you get the rest?