# algebra question

• Sep 22nd 2008, 09:13 AM
Deathscyth3
algebra question
I need help with this problem, I'm unsure as whether to distribute the h or not.

Solve for "a"

D=1/5h(a-b)

As well as this...

An actor invests some money at 7%, and 47,000 more than four times the amount at 12% The total annual interest earned from the investment is 49640. How much did he invest in each amount?
He invested ___ at 7% and ___ at 12%
• Sep 22nd 2008, 09:15 AM
Simplicity
Quote:

Originally Posted by Deathscyth3
I need help with this problem, I'm unsure as whether to distribute the h or not.

Solve for "a"

D=1/5h(a-b)

Form 1: $\displaystyle D = \frac{1}{5h}(a-b)$

or

Form 2: $\displaystyle D = \frac{1}{5h(a-b)}$?
• Sep 22nd 2008, 09:17 AM
masters
Quote:

Originally Posted by Air

Form 1: $\displaystyle D = \frac{1}{5h}(a-b)$

or

Form 2: $\displaystyle D = \frac{1}{5h(a-b)}$?

or

Form 3: $\displaystyle D = \frac{1}{5}h(a-b)$?
• Sep 22nd 2008, 09:18 AM
Deathscyth3
Quote:

Originally Posted by Air

Form 1: $\displaystyle D = \frac{1}{5h}(a-b)$

or

Form 2: $\displaystyle D = \frac{1}{5h(a-b)}$?

It is like the first one except H is not part of the 1/5, it is 1/5 (space) h(a-b)

Its form 3.
• Sep 22nd 2008, 09:23 AM
Simplicity
$\displaystyle D = \frac{1}{5}h(a-b)$

Multiply both sides by $\displaystyle 5$:

$\displaystyle 5D = h(a-b)$

Open the bracket on the right hand side:

$\displaystyle 5D = ha - hb$

Add $\displaystyle hb$ to both sides:

$\displaystyle 5D + hb = ha$

Divide both sides by $\displaystyle h$:

$\displaystyle a = \frac{5D + hb}{h} = \frac{5D}{h} + b$
• Sep 22nd 2008, 09:30 AM
Deathscyth3
done.
• Sep 22nd 2008, 10:06 AM
masters
Quote:

Originally Posted by Deathscyth3
As well as this...

An actor invests some money at 7%, and 47,000 more than four times that amount at 12% The total annual interest earned from the investment is 49640. How much did he invest in each amount?
He invested ___ at 7% and ___ at 12%

Let x = amount invested at 7%.
.07x = interest accumulated

Let 4x + 47000 = amount invested at 12%
.12(4x + 47000) = interest accumulated

Total interest accumulated is given by:

.07(x)+.12(4x+47000) = 49640

Can you finish?