Question

Mr. Jones has $24, 000 to invest. He invests part at 4% and the rest at 6 %. If he earns $1, 200 in interest after1 year, how much did he invest at each rate?Mr. Jones invested $_ at 4% and $_ at 6 %.

Answer 1

Mr. Jones invested $12,000 at 4% and $12,000 at 6%.

Explanation:

Let x be the amount of money invested at 4% and y the amount of money invested at 6%, we can establish the following system of equations:

`\begin{gathered} x+y=24000\rightarrow y=24000-x \\ \\ 4\%x+6\%y=1200\rightarrow0.04x+0.06y=1200 \end{gathered}`

To solve we substitute the first equation in the second equation and solve for x, like this:

`\begin{gathered} 0.04x+0.06(24000-x)=1200 \\ \\ 0.04x+1440-0.06x=1200 \\ \\ -0.02x=1200-1440 \\ \\ x=(-240)/(-0.02) \\ \\ x=12000 \\ \\ \text{ So for y would be:} \\ \\ y=24000-12000 \\ \\ y=12000 \end{gathered}`

This means that Mr. Jones invested $12,000 at 4% and $12,000 at 6%.