Dorothy Divided $14,500 Among Two Accounts Paying 11% And 8% Interest Annually. The Interest Earned After 1 Year In The 8% Account Was $455 Less Than That Earned In The 11% Account. How Much Money Was Invested In Each Account?

[master_senseye]

Dorothy divided $14,500 among two accounts paying 11% and 8% interest annually. The interest earned after 1 year in the 8% account was $455 less than that earned in the 11% account. How much money was invested in each account?

[davebro]

which bank please?

[gingejbee]

Dorothy was very clever to find such high-interest accounts.

[gingejbee]

^ two minds...one thought!

[New Judge]

$8,500 in the 11% account (giving $935 interest)
$6,000 in the 8% account (giving $480 interest)

[davebro]

please show your workings!

[aelmpvw]

well we know for sure that New Judge isn't Diane Abbott

[gingejbee]

...and giving the answer (although proving that you are competent at simple maths) doesn't really help the OP.

[JJ109]

Let x = the amount invested in the 8% account and y = the amount invested in the 11% account.

Now set up a pair of simultaneous equations
We know x + y = $14,500 (equation 1)

We also know that 8%x + $455 = 11% y (equation 2)

From Equation 1 x = 14500 - y
Substitute this value for x in equation 2 which becomes
8%(14500 - y) + 455 = 11% y
Multiply both sides of the equation by 100 as I don't like dealing in percentages!
8(14500 - y) +45500 = 11y
116000 - 8y + 45500 = 11y
161500 = 11y + 8y
161500 = 19y
y = 161500 / 19 = 8500
From equation 1 x + y = 14500
Therefre x = 14500 - 8500 = 6000

$6000 invested at 8% = $480 interest
$8500 invested at 11% = $935 interest

Difference = $935 - $480 = $455 = CORRECT

[pastafreak]

You know you are probably doing the homework of someone who can't be bothered to do the hard work themselves.

[zebo]

She invested it between two accounts, not among, just to nit-pick!

[JJ109]

Yes Pasta - but whenever you get these type of questions for homework the OP will normally have more than one example to do. I believe in giving a clear and consise answer with the methodology in the hope that the OP will then be able to complete the rest themselves.

[Gizmonster]

X + Y = 14500 (Equation 1)
0.08X = A (interest accrued in 8% account) (Equation 2)
0.11Y = B (interest accrued in 11% account) (Equation 3)
The interest earned after 1 year in the 8% account was $455 less than that earned in the 11% account:
B - 455 = A
or B - A = 455 (Equation 4)
Equation 3 minus equation 2 gives:
0.11Y - 0.08X = B - A
Substitute B - A = 455 from equation 4 gives:
0.11Y - 0.08X = 455 (Equation 5)
Multiply equation 1 by 0.08 gives:
0.08X + 0.08Y = 1160 (Equation 6)
Add equation 5 and 6 together gives:
0.11Y + 0.08Y + 0.08X - 0.08X = 1160 + 455
0.19Y = 1615
Divide both sides by 0.19 gives
Y = 8500
Substitute Y = 8500 into equation 1:
X = 6000