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

- anonymous

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- anonymous

all right

- anonymous

begin with 320,000.

- anonymous

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

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- anonymous

rite

- anonymous

let's say X0 represents the debt in 1980

- anonymous

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

- anonymous

oh my you lost me

- anonymous

all right

- anonymous

so, what would be the debt in 1981?

- anonymous

i was just having variables stand in for the amounts

- anonymous

would it be the same as 1980?

- anonymous

the company reduces its debt by 15% each year

- anonymous

so minus 15% each year?

- anonymous

so it'd be less than the year before

- anonymous

right, -15% per year

- anonymous

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

- anonymous

37999.85

- anonymous

is that the answer?

- anonymous

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

- anonymous

total debt in 1981

- anonymous

no, how did you get that?

- anonymous

i minused 15% the debt from 1980

- anonymous

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

- anonymous

319,999.85

- anonymous

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

- anonymous

320,000 - 48,000 = debt in 1981

- anonymous

why multiply?

- anonymous

where did you get 48,000??

- anonymous

.15 * 320,000

- anonymous

you lost me. im sorry im horrible at math

- anonymous

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

- anonymous

are you familiar with percentages?

- anonymous

yes

- anonymous

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

- anonymous

thats how you got 48,000?

- anonymous

yeah. 15% is actually the decimal .15

- anonymous

i know

- anonymous

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

- anonymous

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

- anonymous

so it would be 15% minus 7 years?

- anonymous

not quite

- anonymous

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

- anonymous

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

- anonymous

right

- anonymous

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)

- anonymous

or
debt in 1981 = debt in 1980 * .85

- anonymous

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

- anonymous

its confusing

- anonymous

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

- anonymous

but that is the general set up

- anonymous

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

- anonymous

sure, no problem

- anonymous

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

- anonymous

so we did 1981?

- anonymous

do you think you can try to solve it?

- anonymous

yes

- anonymous

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

- anonymous

oh please give me 10min.

- anonymous

sure

- anonymous

okay i lost myself.

- anonymous

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

- anonymous

so how far did you get?

- anonymous

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

- anonymous

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

- anonymous

we said 480000 before

- anonymous

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

- anonymous

that would be 272000

- anonymous

correct

- anonymous

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?

- anonymous

no

- anonymous

heh, what's up?

- anonymous

you wold minus .15 from 272000??

- anonymous

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

- anonymous

thats what i meant

- anonymous

cool, then you got it

- anonymous

i got 271999.85

- anonymous

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

- anonymous

you simply subtracted .15 from 272,000

- anonymous

you need to multiply then subtract

- anonymous

ugh okay

- anonymous

when i multiply i get 40800

- anonymous

ok. now subtract that from 272,000

- anonymous

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

- anonymous

231200

- anonymous

ok so now for 1983

- anonymous

multiply 231200 * .15

- anonymous

nice
then subtract

- anonymous

196520

- anonymous

solid, and repeat for 1984...

- anonymous

seems like you got It, right?

- anonymous

1984 is 225998

- anonymous

yes

- anonymous

hey, sorry, did you get the rest?

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