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

$1000 was invested at 5%

$4000 was invested at 10%

Step-by-step explanation:

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

The mathematical formula for simple interest is:

`I\text{ = }(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{ }*\text{ }(5)/(100)\text{ = }(5x)/(100)`

For the second part, we have that as:

`(10)/(100)\text{ }*(x\text{ + 3000\rparen = }\frac{10x\text{ + 30000}}{100}`

The sum of these two interests is $450

We have this as:

`\begin{gathered} (5x)/(100)\text{ + }(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{ = }(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