Question

Mr. Jones has $18,000 to invest. He invests part at 5 % and the rest at 8 %. If he earns $1,170 in interest after1 year, how much did he invest at each rate?Mr. Jones invested $___at 5% and $___at 8 %.

Answer 1

Amount invested at 5% = $9,000

Amount invested at 8% = $9,000

Step-by-step explanation:

Let the amount of the 5% investment be x.

So the amount of the 8% investment will be (18000 - x)

If he earned $1170 interest after 1 year, we can go ahead and determine the value of x by setting up the below equation;

`0.05\cdot x+0.08\cdot(18000-x)=1170`

If we expand the parentheses, we'll have;

`\begin{gathered} 0.05x+1440-0.08x=1170 \\ -0.03x+1440=1170 \end{gathered}`

Let's subtract 1140 from both sides of the equation;

`\begin{gathered} -0.03x=1170-1440 \\ -0.03x=-270 \\ \end{gathered}`

Let's divide both sides by -0.03;

`\begin{gathered} (-0.03x)/(-0.03)=(-270)/(-0.03) \\ x=9000 \end{gathered}`

We can see that Mr. Jones invested $9,000 at 5%.

So the amount he invested at 8% will be;

`18000-x=18000-9000=9000`

We can also see that the amount invested at 8% was $9,000