Thread: Investing her bonus

Please help me find the equation to work out this problem. Your help is much appreciated.

Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?

To learn how to set up and solve this sort of exercise, try here.

Then:

. . .invested:
. . . . .at 4%: x
. . . . .at 2.25%: 33,000 - x

. . .interest:
. . . . .at 4%: 0.04x
. . . . .at 2.25%: ??(33,000 - x)

Complete the table. Sum the two interest expressions, and set equal to the given total. Then solve the linear equation. Back-solve for the required values.

Originally Posted by stapel

To learn how to set up and solve this sort of exercise, try here.

Then:

. . .invested:
. . . . .at 4%: x
. . . . .at 2.25%: 33,000 - x

. . .interest:
. . . . .at 4%: 0.04x
. . . . .at 2.25%: ??(33,000 - x)

Complete the table. Sum the two interest expressions, and set equal to the given total. Then solve the linear equation. Back-solve for the required values.

Thanks for the link. I set up a table. The 2.25% threw me a bit. It took me a few attempts before I realized I just needed to set 2.25% to just 0.02, not 0.0225, nor 0.023.

Out of the table, I ended up working out the following:
0.04+0.02(33000-x)=970
0.04x+660-0.02x=970
660+0.02x=970
0.02x=310
x=15500

y=33000-15500=17500
y=17500

So she invested $15,500 at the 4% rate.
She invested $17,500 at the 2.25% rate.

Does this look correct?

The answer to any "solving" exercise can be checked by plugging it back into the original question. So plug the values into the "simple interest" formula, and verify that the interest amounts sum to the correct value.

Originally Posted by dkpeppard

It took me a few attempts before I realized I just needed to set 2.25% to just 0.02, not 0.0225, nor 0.023.

Your answer is incorrect.
HOW in heck did you realise that?! 2.25% is .0225 (nothing else!).
.04x + .0225(33000 - x) = 970

Originally Posted by Wilmer

Your answer is incorrect.
HOW in heck did you realise that?! 2.25% is .0225 (nothing else!).
.04x + .0225(33000 - x) = 970

When I multiply 0.0225*33000 I get 742.50. For some reason the decimal was throwing me off, so I thought I needed to round the interest up from 0.0225 to 0.02 to get an even value of 759.

Ok, I reworked the problem and got the following.

0.04+0.0225(33000-x)=970
0.04x+742.50-0.02x=970
742.50+0.0175x=970
0.0175x=227.50
x=13000

y=33000-13000=20000
y=20000

So,
For the 4% rate she invested $13000.
For the 2.25% rate she invested $20000.

Thank you for help guide me. Not sure why I got so hung up on the decimal in the problem last night.

C'est correct. Bien fait!