Question

Dillon plans to invest $16,000 part at 4% simple interest and the rest at 5% simple interest what is the most he can invest at 4% and still be guaranteed at least 700 per year

Answer 1

Answer:

The most Kyle can invest at 4% is $10000.

Step-by-step explanation:

To Determine:

What is the most he can invest at 4% and still be guaranteed at least $700 in interest per year?

Information Fetching and Solution Steps:

As

• Dillon plans to invest $16,000 part at 4% simple interest

• and the rest at 5% simple interest

So,

If Kyle has to invest $16,000. then the following equations can be established from the given data

$x + y = 16,000$

$.04x + .05y = 700$

Multiplying the second equation by 100, we get,

$4x+5y = 70000$

Multiplying the 1st equation i.e. $x + y = 16,000$ by 5

$5x + 5y = 80000$

So, the equations become

$\begin{bmatrix}5x+5y=80000\\ 4x+5y=70000\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:5x+5y=80000:\quad x=16000-y$

As

$5x+5y=80000$

$5x+5y-5y=80000-5y$

$5x=80000-5y$

$\frac{5x}{5}=\frac{80000}{5}-\frac{5y}{5}$

$x=16000-y$

$\mathrm{Subsititute\:}x=16000-y$

$\begin{bmatrix}4\left(16000-y\right)+5y=70000\end{bmatrix}$

$\mathrm{Isolate}\:y\:\mathrm{for}\:4\left(16000-y\right)+5y=70000:\quad y=6000$

As

$4\left(16000-y\right)+5y=70000$

$64000-4y+5y=70000$

$64000+y=70000$

$y=6000$

$\mathrm{For\:}x=16000-y$

$\mathrm{Subsititute\:}y=6000$

$x=16000-6000$

$x=10000$ $

Therefore, the most Kyle can invest at 4% is $10000.

Keywords: interest rate, equation

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