Question 21050
Try this:
Let x = the amount invested at 8% (0.08).
The interest on this amount is written as: 0.08x
Let (24000 - x) = the amount invested at 7.2% (0.072).
The interest on this amount is written as: 0.072(24000 - x)

The interest on the 8% part is 2/3 the interest on the 7.2% part.
So, you can say: {{{0.08x = 0.072(24000-x)(2/3)}}}

Now you can write the equation to solve this problem:

{{{0.08x + 0.072(24000 - x) = 0.072(24000 - x) + 0.072(24000 - x)(2/3)}}} Simplify.
{{{0.08x + 1728 - 0.072x = 0.072(24000 - x)(5/3)}}}
{{{0.008x + 1728 = (5/3)(1728 - 0.072x)}}}
{{{0.008x + 1728 = 2880 - 0.12x}}} Add 0.12x to both sides.
{{{0.128x + 1728 = 2880}}} Subtract 1728 from both sides.
{{{0.128x = 1152}}} Finally, divide both sides by 0.128
{{{x = 9000}}}

So, $9,000.00 was invested at 8% and ($24,000.00 - $9,000.00 = $15,000.00) was invested at 7.2%

Check:

0.08($9,000.00) = $720.00 The interest on the amount invested at 8%
0.072($15,000.00) = $1,080.00 The interest on the amount invested at 7.2%.

{{{(2/3)(1080) = 720}}} Checks ok.