SOLUTION: Isabella sends money to each niece and nephew on his or her b'day. She gives each child $10.00 on his or her 1st b'day. On each b'day thereafter, you and your cousins get $20.00 mo

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Isabella sends money to each niece and nephew on his or her b'day. She gives each child $10.00 on his or her 1st b'day. On each b'day thereafter, you and your cousins get $20.00 mo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 502147: Isabella sends money to each niece and nephew on his or her b'day. She gives each child $10.00 on his or her 1st b'day. On each b'day thereafter, you and your cousins get $20.00 more than the b'day before. How old will you be when you have rec'd a total of $4,000.00 form Aunt Isabella?
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
1st Birthday I received = $10
2nd Birthday I received = $30
3rd Birthday I received = $50
4th Birthday I received = $70
And so on
10+30+50+70+…………. To sum of 4000
This is an arithmetic progression so we will use the following formula
s= n/2[2a+(n-1)d]
where
s = sum of progression= 4000
n = number of terms = ?
a = value of first term = 10
d = difference between two terms = 20
Plug in the values in the formula
s= n/2[2a+(n-1)d]
4000=n/2[(2*10)+(n-1)20]
4000=n/2[20+(20n-20)]
4000=(n/2)(20+20n-20)
4000=(n/2)(20n)
4000=20n^2/2
4000=10n^2
Divide by 10 both sides of the above equation
4000/10=10n^2/10
400=n^2
Taking square root both sides of the equation
√400=√n^2
20=n
n=20
On my 20th birthday I will have received total amount of $4000.00 from Aunt Isabella.