At the age of 21, Cyndi began receiving yearly payments from a trust fund. On each succeeding birthday, she received twice as much as in the preceding year. If she had received a total of $303,800 by age 25, how much did she receive at age 21?
How do I do this?
2007-04-30 13:21:39 · 4 answers · asked by ♥ Mommy To Be 12/20/09 ♥ 3 in Science & Mathematics ➔ Mathematics
Supposed she received $x at age 21. Then at ages 22, 23, 24 and 25 she would have received 2x, 4x, 8x and 16x respectively, for a total of 31x over the five years. So x = 303800/31 = 9800. So she received $9,800 at age 21.
In general, if it's more than a few terms you'd need to use the formula for the sum of a geometric series:
Sn = a(1 - r^n) / (1 - r)
303800 = a (1 - 2^5) / (1 - 2)
=> a = 303800 (-1/-31) = 9800.
2007-04-30 13:25:24 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
years
21 = x amount of money
22 = x + 2x
23 = x + 2x + 2(x + 2x)
24 = x + 2x + 2(x+2x) + 2(x + 2x + 2(x+2x))
25 = x + 2x + 2(x+2x) + 2(x + 2x + 2(x+2x)) + 2(x + 2x + 2(x+2x) + 2(x + 2x + 2(x+2x)))
Looks hard, but it is easy.
so simplify:
21 = x
22 = 3x
23 = 3x + 2x + 4x
= 9x
24 = 9x + 18x
= 27x
25 = 27x + 54x
= 81x
303,800 = 81x
x = (around) $3750.62.
2007-04-30 13:35:19 · answer #2 · answered by flit 4 · 0⤊ 0⤋
since she started at age 21 she has recieved money for 5 years (21,22,23,24,25)
and each year she got twice as much so your equation would look like this...
x + 2x + 2(2x) + 2(2(2x)) +2(2(2(2x))) = 303,800
I hope this helps.
2007-04-30 13:27:35 · answer #3 · answered by balgne 3 · 0⤊ 0⤋
x*2^4=303,800
x=18,987.50
2007-04-30 13:26:32 · answer #4 · answered by leo 6 · 0⤊ 1⤋