SOLUTION: Your favorite aunt put money into a savings account for you. The account earns simple interest; that is, it increases by a fixed amount each year. After 2 years your account has $8

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Question 908727: Your favorite aunt put money into a savings account for you. The account earns simple interest; that is, it increases by a fixed amount each year. After 2 years your account has $8250 and after 5 years it has $9375.
The question asks to construct an equation and find the initial principal.
we have been using the formula is Y= M(x)+b. i do not understand what to use or how to find the equation.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll use my own symbols- you can
convert them to the ones you use
Let +P+ = the principal
Let +x+ = the simple interest earned each year
I can say:
After 2 yrs:
(1) +8250+=+P+%2B+2x+
After 5 yrs:
(2) +9375+=+P+%2B+5x+
---------------------
This is 2 equations and 2 unkowns,
so it is solvable
Subtract (1) from (2)
(2) +9375+=+P+%2B+5x+
(1) +-8250+=+-P+-+2x+
+1125+=+3x+
+x+=+375+
----------------
And
(1) +8250+=+P+%2B+2x+
(1) +8250+=+P+%2B+2%2A375+
(1) +8250+=+P+%2B+750+
(1) +P+=+7500+
The principal was $7,500
-------------------------
The rate of simple annual interest is:
+375+%2F+7500+=+.05+ or 5%
--------------------------
I think the equation they want is:
+A+=+7500+%2B+.05%2A7500%2An+
Where +A+ = the amount you have
in the account after +n+ years
For instance:
After +5+ years:
+A+=+7500+%2B+.05%2A7500%2A5+
+A+=+7500+%2B+1875+
+A+=+9375+
OK