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Question 165348: Hi,
I can't seem to find a solution to this word problem:
"A man invests a certain sum of money at 14% and twice that amount at 15%. If his total interest earnings are $660 per year, how much has he invested at 14% and how much at 15%?"
I don't even know where to begin. Word problems are one of my weakest topics.
Thanks,
Jane
Found 2 solutions by nerdybill, Earlsdon:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! "A man invests a certain sum of money at 14% and twice that amount at 15%. If his total interest earnings are $660 per year, how much has he invested at 14% and how much at 15%?"
.
Let x = amount invested at 14%
then
2x = amount invested at 15%
.
.14x + .15(2x) = 660
.14x + .30x = 660
.44x = 660
x = 660/.44
x = $1500 (amount invested at 14%
.
Amount invested at 15%:
2x = 2(1500) = $3000 (amount invested at 15%)
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! Ok, Jane, here's how you would set up this kind of problem:
As is common in algebra, you assign a variable (letter) to represent the unknown amount.
Let's call this amount x and this is the amount that the man invested at a rate of 14%. You are also told the he invested twice that amount (that's 2*x) at a rate of 15%.
You are further told the the total amount of interest earned on these two amounts is $660.00
So, we need a way to express the amount of interest earned on these two amounts that were invested.
Remember that the amount interest earned of a sum of money (called the Principal) is simply P times the interest rate (i) and for the first amount, P = x (x is because we don't know the number of dollars yet) and the interest rate is given as 14%, so, first change the percent to its decimal equivalent (14% = 0.14) and multiply it by the principal, P (x dollars).
Similarly for the second amount (2x dollars) and interest rate of 15% (15% = 0.15) to get:
Now we'll add these two amounts, the sum of which is equal to $660.00
 Now we have an equation in x that can be solved.
 Combine the x-terms on the left side.
 Divide both sides by 0.44
So the man invested $1,500.00 at 14% and $3,000.00 at 15 %
Check:
0.14($1,500)+0.15($3,000) = $210+$450 = $660.00 This is the total amount earned.
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