# Profit problem.

#### bergausstein

##### Active member
A small firm borrows \$1000 from a stockholder at a sim-pleinterest rate of 7.5%. The company secretary lends the firm an additional sum at a simple interest rate of 8.25%. At the end of one year, the firm repays a total of \$3997.75. How much did the secretary lend the firm and
what is the simple interest rate on the total loan?

let

$y=$ additional money lent

$1000+y =$ total amount of money lent.

$1000(0.075)+0.0825y=3997.75$

$0.0825y=3997.75-75$

$y=47,548.48$ - additional money lent.

$1000+47,548.84 = 48548.48$ total amount of money lent.

$\frac{3997.75}{48548.48}=0.823=8.23\%$ interest rate on the total loan.

i just want to confirm if my solution is correct. thanks!

#### LATEBLOOMER

##### New member
Re: ALGEBRA Profit problem.

it's not correct! Last edited:

#### bergausstein

##### Active member
Re: ALGEBRA Profit problem.

#### mente oscura

##### Well-known member
Re: ALGEBRA Profit problem.

Hello.

Stockholder: 1000.00

Interest stockholder:$$\ 1000.00*0.075=75.00$$

Secretary= x

Interest secretary= 0.0825x

It tries to continue.

Regards.

#### bergausstein

##### Active member
Re: ALGEBRA Profit problem.

that's what i do above.

i added $75+0.0825y=3997.75$ then $y=47548.48485$

what's wrong with my solution?

#### mente oscura

##### Well-known member
Re: ALGEBRA Profit problem.

that's what i do above.

i added $75+0.0825y=3997.75$ then $y=47548.48485$

what's wrong with my solution?
Hello.

A small firm, at the end of one year, the firm repays a total of $3997.75. (The amount + interests) Repays: 1000.00+75.00+x+0.0825x=3997.75 For all these questions, you thinks that it is your money, and you will see like you are not wrong. If you give 1000.00$ to one year, to an interest rate. You are satisfied if only they give you the interests?

It tries to continue. Regards.

#### bergausstein

##### Active member
Re: ALGEBRA Profit problem.

the additional money lent is \$2700 the total money lent is \$3700.

simple interest rate of total loan is

$0.0825(y)+75=0.0825(2700)+75=297.75$

the simple interest rate for the total loan is 8% am i correct?

#### mente oscura

##### Well-known member
Re: ALGEBRA Profit problem.

the additional money lent is \$2700 the total money lent is \$3700.

simple interest rate of total loan is

$0.0825(y)+75=0.0825(2700)+75=297.75$

the simple interest rate for the total loan is 8% am i correct?
Yes.

8.047%

Regards.

#### MarkFL

Staff member
Re: ALGEBRA Profit problem.

...
It tries to continue...
Have you ever seen the movie The Silence of The Lambs? Your wording there puts me in mind of a character in the movie.

#### mente oscura

##### Well-known member
Re: ALGEBRA Profit problem.

Have you ever seen the movie The Silence of The Lambs? Your wording there puts me in mind of a character in the movie. What?

Yes.

Yes, I have seen the movie. Whom do I him resemble? Regards.

#### MarkFL

Staff member
Re: ALGEBRA Profit problem. What?

Yes.

Yes, I have seen the movie. Whom do I him resemble? Regards.
Do you recall the serial killer "Buffalo Bill" that was keeping the young woman in a pit in his basement, and he would say things like:

"It rubs the lotion on its skin..."

"It puts the lotion in the basket..."

When you stated, "It tries to continue," I thought of this character. I do apologize to the OP for hijacking the thread, but I just couldn't resist interjecting a bit of humor here and the thread seemed to have run its course.

#### HallsofIvy

##### Well-known member
MHB Math Helper
A small firm borrows \$1000 from a stockholder at a sim-pleinterest rate of 7.5%. The company secretary lends the firm an additional sum at a simple interest rate of 8.25%. At the end of one year, the firm repays a total of \$3997.75. How much did the secretary lend the firm and
what is the simple interest rate on the total loan?

let

$y=$ additional money lent

$1000+y =$ total amount of money lent.

$1000(0.075)+0.0825y=3997.75$
This is incorrect. The left side is the interest accrued over the year. The right side is the total principle and interest. They are NOT equal.

$0.0825y=3997.75-75$

$y=47,548.48$ - additional money lent.

$1000+47,548.84 = 48548.48$ total amount of money lent.

$\frac{3997.75}{48548.48}=0.823=8.23\%$ interest rate on the total loan.

i just want to confirm if my solution is correct. thanks!