word problem

Question

You invest an amount of money at an annual simple interest rate of 4.5%. You invest a second amount, $1000 more than the first, at an annual simple interest rate of 7.5%. Let x represent the amount invested at 4.5%

Answer 1

Then the formula you need is 0.12X + 75

 

----------------------------------------------------- <--- that's the short answer

 

PROOF:

4.5% = 0.045 and 7.5% = 0.075

 

So the statement is translated as:

 

        0.045X  + 0.075(X+1000) =

        0.045X + 0.075X + 75 =

        0.12X + 75

 

Now to CHECK IT, let X=1000. Then $2000 is invested in the second account.

The expressions evaluates as

 0.045(1000) + 0.075(2000) = 45 + 150 = 195.

The RESULT is 0.12*1000 + 75 = 120+75=195 so yes it checks.

 

You may use 0.12X + 75 as the algebraic expession

 

[End of Proof]

==========================================

Typically you are told the return of interest for the two accounts.

Once you find that data, set it equal to the expression I have

derived for you in bold and solve for x.

 

For example, suppose the combined return of interest is $111.

Then 0.12X+75 = 111

        0.12X = 36

         12X = 3600

         X = 300

So 300 is invested in the first account and 1300 in the second.

The return is 0.045(300) + 0.075(1300) = 13.50 + 97.50 =  111

 

[End of Proof]