Question

suppose we invest x dollars at 5% annual simple interst and $3000 more at 10%. After one year we find that our total interst is $450. how much did we invest at each rate

Answer 1

Answer:

$1000 was invested at 5%

$4000 was invested at 10%

Explanation:

Here, we want to calculate the amount invested at each rate

The mathematical formula for simple interest is:

$I\text{ = }\frac{PRT}{100}$

Where:

P is the amount invested which

R is the rate of investment

T is the time (1 in this case)

For the first $x, we have the interest as:

$x\text{ }\times\text{ }\frac{5}{100}\text{ = }\frac{5x}{100}$

For the second part, we have that as:

$\frac{10}{100}\text{ }\times(x\text{ + 3000\rparen = }\frac{10x\text{ + 30000}}{100}$

The sum of these two interests is $450

We have this as:

$\begin{gathered} \frac{5x}{100}\text{ + }\frac{10x+30000}{100}\text{ = 450} \\ \\ 5x\text{ + 10x + 30000 = 100\lparen450\rparen} \\ 15x\text{ + 30000= 45000} \\ 15x\text{ = 45000-30000} \\ 15x\text{ = 15000} \\ x\text{ = }\frac{15000}{15} \\ x\text{ = \ 1,000} \end{gathered}$

The value of x is 1000, while the value of x+ 3000 (3000 more) is 4,000