help with algebra word problem?

Question

Between 1992 and 1999, you added approximately 15 stamps per year to your collection. In 1997 you had 130 stamps. Find an equation that represents the number of stamps in your collection, y, in terms of the year, t. Let t=0 correspnd to 1992.

Answer 1

This can be considered as a problem of Arithmetic progression.
Hence, the common difference d=15. Number of years of stamp between 1992to 1999 is 8 years. then n=8
It is already known that Tn the last term = 130
ie, 130= [a +( n-1)*d] ; where a is the first term of the series.
Substituting the known values we have
130=[a + (8-1)15]
consequently, a=25
Then formula for the total number of collection of stamps on the n th year is Tn = [25 +(n-1)15]
or y= 25 +(t-1)15; as you have desired the formula to be in this form.

Answer 2

oookay. first I'd find how many stamps you started with.

130 stamps in 1997 hmmm.

1997 - 1992 = 5. you could use 6 though because they aren't stating at what time during the years the collection is being counted. I'll use 6. ( one of those lame grey areas )

6 * 15 ( per year ) = 90 stamps from 1992 to 1997.

130 - 90 = starting amount. or 40 stamps in beginning of 1992.

hmmm

number of stamps = year * 15 + 40..

but they want 1992 to be 0 not 1.. so we'll have to add the 15 stamps up front to 1992 .. so,

number of stamps = year * 15 + 55..

or

y = t * 15 + 55

lets test it.

year 1997 would be t=5 ( 97-92 )

so y = t * 15 + 55
y = 5* 15 + 55
y = 75 + 55
y = 130

and from the question we know there were 130 stamps in 1997. So it seems to work :D

Answer 3

y = 1999 - (1992 + 1997)/t + 130*15t

Easy.

Answer 4

let the eq representing be

at^2 + bt + c

at t=0, we have no stamps in our collection so c=0;

now the eq is reduced to --------at^2 + bt

it`s avg over the 7 ers is 15

so integration(0,7)[at^2+bt]=15*7=total no of stamps after 7 ers.

2at^3+bt^2 over (0,7ers)=15*7----------(1)

now at t=5 , at^2 + bt =130 (given)--------(2)

solve above 2 eq by putting the values of t and the for a & b.
and get the eq.mail
mail me ans if u get it.

Answer 5

let x be the number of stamps that u had first

then

total=x+(t*15)

i think this is it