Question

A portion of $ 100,000 (x) was invested with a 3% after one year. The rest of the investment (y) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the 100,000 were divided? 3) how much money was invested at a 3% rate of return? 4) How much money is at a rate of return of 1%?

Answer 1

Given :

A portion of $ 100,000 (x) was invested with a 3% after one year.

The rest of the investment (y) obtained a return of 1%.

So, the rest y = 100,000 - x

The total return = 1800

So,

3% of x + 1% of y = 1800

1) What equation shows the return on investment?

The equation will be:

`\text{0}.03x+0.01y=1800\rightarrow(1)`

2) What equation shows how the 100,000 were divided?

The equation will be:

`x+y=100000\rightarrow(2)`

Solve the previous equation to find the part (3) and (4)

so,

From the second equation: y = 100,000 - x

Substitute with x into equation (1)

So,

`\text{0}.03x+0.01(100000-x)=1800`

Solve the equation to find x:

`\begin{gathered} 0.03x+0.01\cdot100000-0.01x=1800 \\ \text{0}.02x+1000=1800 \\ 0.02x=1800-1000 \\ \text{0}.02x=800 \\ \\ x=(800)/(0.02)=40000 \end{gathered}`

Substitute with x into the equation (2) to find y

`\begin{gathered} 40000+y=100000 \\ y=100000-40000 \\ \\ y=60000 \end{gathered}`

3) how much money was invested at a 3% rate of return?

The answer will be x = $40,000

4) How much money is at a rate of return of 1%?​

The answer will be y = $60,000