Problem Solving

AAPL wrote:In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

A. 5
B. 25
C. 200
D. 205
E. 210

John $250 in his account in 2006 and in 2008 he has $270 in his account,
So, in 2 years, John's balance increases by $20
So, the balance increases $10 EACH YEAR

In 2001, John invests x dollars in a special account that yields y% simple interest annually
John's balance increases $10 EACH YEAR
In 2006, John had $250
So, in 2005, John had $240
in 2004, John had $230
in 2003, John had $220
in 2002, John had $210
in 2001, John had $200
In other words, x = 200

So, John's initial investment was $200 and the simple interest is $10/year
$10/$200 = 5/100 = 5%
So, the annual interest rate is 5%
In other words, y = 5

What is x + y?
x + y = 200 + 5
= 205

Answer: D

Cheers,
Brent

AAPL wrote:Magoosh

In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

A. 5
B. 25
C. 200
D. 205
E. 210

OA D.

John's account has $250 in 2006, i.e., after 5 years.

Thus, he invested $x at the rate of y% per annum at simple interest for 5 years, which gave $(250 - x) as simple interest.

=> 250 - x = (x * y * 5) / 100

5000 - 20 x = xy ------(1)

Since account balance in 2008 is $270 and that in 2006 is $250, he earned $20 as simple interest on $x for 2 years at the rate of y% per annum.

=> 20 = (x * y * 2) /100

xy = 1000 ------(2)

Plugging-in the value of xy in equation (1), we get

5000 - 20 x = 1000

=> x = 200

Plugging-in the value of x in equation (2), we get

x = 5

Thus, x + y = 205

The correct answer: D

Hope this helps!

-Jay
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AAPL wrote:Magoosh

In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

A. 5
B. 25
C. 200
D. 205
E. 210

Since he has $250 in his account in 2006 and $270 in 2008, it must be true that the amount of interest is $20 during these two years. Since it's a simple interest, it must mean the amount of interest is $10 per year.

Therefore, in 2001, 5 years before 2006, it must have accumulated $50 in interest, which means the amount in 2001 is $200. So x = 200. Since 10/200 = 5/100 = 5%, y = 5. Therefore, x + y = 205.

Answer: D