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Stini

Member

Registered: 2007-01-23

Posts: 2

algebra Help

I am horrible at word problems please help me... I have 5 weeks to finish my algebra class so the sooner the better
I have the answer I need help on how to get there please help me with figuring out how to get to the answer.

Problem #1 answer = $7000@11%;profit $3000
Sam M. invested part of his $10,000 bonus in a fund that paid 11% profit and invested the rest in stock that suffered a 4% loss. Find the amount of
each investment if his overall net profit is $650.

Problem #2 answer =  30,000@8%;24,000@10%
How can $54,000 be invested, part at 8% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts will be equal?

Problem #3 answer = 400 0uncesHow much of an alloy that is 20% copper should be mixed with 200 ounces of an alloy that is 50% copper in order to get an alloy that is 30% copper?

Problem # 4 answer = 4500
If $3000 is invested at 6% annual simple interest, how much should be invested at 9% annual simple interest so that the total yearly income from both investments is $585?

Problem # 5 answer = 1and 5/7hr
Nedra and latonya Dominguez are 12 miles apart hiking toward each other. How long will it take them to meet if Nedra walks at 3 mph and Latonya walks at 1 mph faster?

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: algebra Help

Problem 1:

Let P = the amount that he invested in the profitable company
Then 10000-P = the amount that he invested in the other company

The profit (or loss) would be .11P for the profitable company and -.04(10000-P) for the other.   The sum of these is 650

.11P + -.04(10000-P) = 650
.11P - 400 + .04P = 650
.15P = 1050
P=7000

He invested in the 7000 in the profitable company ($770 profit) and 3000 in the other company ($120 loss).

Last edited by pi man (2007-01-24 03:16:57)

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: algebra Help

Problem #2 answer =  30,000@8%;24,000@10%
How can $54,000 be invested, part at 8% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts will be equal?

Let P = the amount invested in the first company.   The 54000 - P is the amount invested in the second company.   The profits of the 2 companies are .08P and .10(54000-P).   The profits are equal:

.08P = .10(54000)-P
.08P = 5400 - .1P
.18P = 5400
P = 30000

30000 was invested in the company that earned 8% for a profit of 2400.
24000 was invested in the company that earned 10% for a profit of 2400.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: algebra Help

Problem #3 answer = 400 0unces  How much of an alloy that is 20% copper should be mixed with 200 ounces of an alloy that is 50% copper in order to get an alloy that is 30% copper?

Let X be the amount in ounces of the 20% copper you are adding.  The total weight of the 30% alloy would then be 200 + x.

(.20)X + (.50)200 = (.30)(200 + X)
.2X + 100 = 60 + .3X
40 = .1X
X=400

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: algebra Help

Problem # 4 answer = 4500
If $3000 is invested at 6% annual simple interest, how much should be invested at 9% annual simple interest so that the total yearly income from both investments is $585?

The $3000 you invested at 6% will earn you $180.   You need to earn $585 - 180 = $405 from you other investment.  If X is the amount you invest in the 2nd company at 9%

(.09)X = $405
X= $4500

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: algebra Help

Problem # 5 answer = 1and 5/7hr
Nedra and latonya Dominguez are 12 miles apart hiking toward each other. How long will it take them to meet if Nedra walks at 3 mph and Latonya walks at 1 mph faster?

Nedra walks 3 mph and Latonya walks 4 mph.   When they meet the sum of the distances they walked is 12 miles and they are approaching each other at a rate of 7 mph.   So at a speed of 7mph, it takes 1 and 5/7 hour to cover 12 miles (12/7 = 1 5/7)

Another way to look at it:

Let T equal the time it takes to meet.    Nedra will walk 3T in that time and Latonya will walk 4T.   Together the distance they cover is 12 miles.  3T + 4T = 12;   7T = 12; T = 1 5/7

Stini

Member

Registered: 2007-01-23

Posts: 2

Re: algebra Help

thank you so much, I really appreciate it