# Hi, rather easy systems of equations problem that I would love help on

• February 11th 2009, 11:48 AM
lahoo
Hi, rather easy systems of equations problem that I would love help on
thanks for looking!

http://img.skitch.com/20090211-d4hme...ddtdmamj69.jpg

Please say what equations you used. Thanks a lot, I love this site!
• February 11th 2009, 12:58 PM
Soroban
Hello, lahoo!

Quote:

Person X invested $10,000 in three accounts. . . Account A pays 4.5% interest. . . Account B pays 6.2% interest. . . Account C pays 3.5% interest. X decides to invest into account B double the sum of the other two accounts. When the first dividends came, they earned$549 interest.
How much invested into each account?

If we organize the information, everything is clearer . . .

. . $\begin{array}{|c|c|c||c|} \hline
\text{Account} & \text{Amount} & \text{Rate} & \text{Interest} \\ \hline\hline
A & x & 0.045 & 0.045x \\ \hline
B & 2x+2y & 0.062 & 0.062(2x+2y) \\ \hline
C & y & 0.035 & 0.035y \\ \hline\hline
\text{Total} & 10,\!000 & & 549 \\ \hline \end{array}$

In the second column, we have: . $x + (2x + 2y) + y \:=\:10,\!000 \quad\Rightarrow\quad 3x + 3y \:=\:10,\!000\;\;{\color{blue}[1]}$

In the last column: . $0.045x + 0.062(2x+2y) + 0.35y \:=\:549 \quad\Rightarrow\quad 0.169x + 0.159y \:=\:549$

Multiply by 1000: . $169x + 159y \:=\:549,\!000\;\;{\color{blue}[2]}$

Solve the system of equations: . $\begin{array}{cccc}3x + 3y &=& 10,\!000 & {\color{blue}[1]} \\
169x + 159y &=& 549,\!000 & {\color{blue}[2]} \end{array}$

. . $\begin{array}{cccccc}\text{Multiply }{\color{blue}[1]}\text{ by -53:} & \text{-}159x - 159y &=& \text{-}530,\!000 \\
\text{Add }{\color{blue}[2]}\!: & 169x + 159y &=& 549,\!000 \end{array}$

And we get: . $10x \:=\:19,\!000 \quad\Rightarrow\quad x \:=\:\boxed{\1900}$ in account $A.$

Substitute into [1]: . $3(1900) + 3y \:=\:10,\!000 \quad\Rightarrow\quad y \:=\:\frac{4300}{3} \:=\:\boxed{\1433.33}$ in account $C.$

Then: . $2(1900 + 1433.33) \;=\;\boxed{\6666.67}$ in account $B.$