last year pete decided to invest half of his money in a credit union paying4.5% inrest,one third of his money in a mutual fund paying 5% intrest,and the rest of his money in a bank CD paying 4% intrest.if his annual investment income was 357.50 last year,how much money had he invested?
2007-02-22 12:19:01 · 7 answers · asked by sinajina 1 in Science & Mathematics ➔ Mathematics
Lets say the total money that pete had in the beginning is X
Then he invested 1/2 X in credit union.
He then invested 1/3 X in mutual fund.
The remaining money he has is 1- 1/2 X - 1/3 X = 1- 5/6 X = 1/6X
Interest = 1/2X *4.5/100 + 1/3X *5/100 + 1/6 X *4/100
= 1/600 X (3*4.5 + 2*5 + 1*4)
=1/600 X (13.5 +10 +4)
1/600 X (27.5) = 357.5
X = 357.5 *600/27.5
=7800
So Pete invested 7800
2007-02-22 12:30:25 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Whatever the solution to (0.045)(1/2)x + (0.05)(1/3)x + (0.04)(1 - 1/2 - 1/3)x = 357.50 is. I'd convert all decimals to fractions, instead of fractions to decimals, since the decimal for 1/3 would have to be rounded off.
Ok, I'll do it. But you better LEARN something from this besides what the answer is.
4.5% is the same as 4.5 out of 100, or 4.5/100. That's an ugly fraction, so multiply the top and bottom by 10 to kill the decimal and get 45/1000. Reduce this to get 9/200.
Similarly, 5% is 1/20 and 4% is 1/25.
So you want to solve
(9/200)(1/2)x + (1/20)(1/3)x + (1/25)(1/6)x = 357 1/2
the 1/6 comes from 1 - 1/2 - 1/3, the "rest" invested at 4%.
Multiply the three pairs of fractions to get
(9/400)x + (1/60)x + (1/150)x = 715/2
The 715/2 is the improper fraction version of 357.50.
Next, I'd kill all the fractions by mutliplying everything by the LCD. It's not obvious, but it's 1200. When you multiply each fraction by 1200, you should be able to cancel each denominator. For example, in
(9/400)*1200,
the 400 cancels into the 1200, leaving behind a 3. Multiply this times the 9 to get 27.
Anyways, hit eveything with 1200 to kill all the fractions and get
27x + 20x + 8x = 429,000
Add the x's to get
55x = 429,000
Divide by 55 to get
x = $7800 EXACTLY.
(Yes, you probably could have gotten clsoe enough to $7800 using strictly decimals. But I have ZERO fear of fractions.)
I hope you get a better idea of HOW to approach this problem, and not just write down an answer for a few points on a homework assignment that means nothing in the big scheme of things.
2007-02-22 12:37:44 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Let the invisted money is x
then his annual investment income will be :
x (.5 * 4.5 /100 + 1/3 * 5/100 + ( 1 - 1/2 - 1/3 )* 4/100) = 357.5
x ( 2.25 + 5/3 + 2/3) = 35750
x ( 55/12) = 35750
x = 35750 × 12/55
x = 7800
2007-02-22 12:38:06 · answer #3 · answered by a_ebnlhaitham 6 · 1⤊ 0⤋
assume total money pete's has is x
3/6 x * 4.5% + (2/6) x * 5% + (1/6) * 4% = 357.50
.0225x + 0.0167x + 0.0067x = 357.50
0.0459 x = 357.50
x = $ 7788.67
he invested $ 7,788.67
2007-02-22 12:26:25 · answer #4 · answered by Blue Moon 3 · 0⤊ 1⤋
he invested £7,800
Half of it (£3,900) @ 4.5% = £175.50
A third of it (£2,600) @ 5% = £130.00
the balance (£1,300) @ 4% = £52.00
total = £175.50 + £130.00 + £52.00 = £357.50
2007-02-22 12:36:50 · answer #5 · answered by mainwoolly 6 · 0⤊ 0⤋
Let the principal be X and times is represented by a period .
(0.5X . 0.045) + (0.3333X . 0.05) + (0.1667X . 0.04) = 357.5
0.0225X + 0.016665X + 0.006668X = 357.5
0.045833X = 357.5
X = 357.5 / 0.045833 = 7800
2007-02-22 13:05:42 · answer #6 · answered by narkypoon 3 · 1⤊ 1⤋
50% less than he would admit to the government!
2007-02-22 12:24:34 · answer #7 · answered by Chris W 4 · 0⤊ 1⤋