Setting an up equation from word problems...

Justaguy

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Sep 18, 2010
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Hi folks, first time posting. What an incredible resource! Anyway, I have two problems that have been bugging me, and I think I got the first one. Here they are:

(1) Charles has had two accounts for a year, one is a savings account at a credit union, that pays 4% annual interest. The other is a money market account, that pays 6% annual interest. Charles deposited $500 more in the money market account than in the savings account. The total interest that he obtained at the end of one year was $160. How much money did he deposit in each account?


(2) A total investment of $13,500 is distributed in two accounts, one that yields interest at an annual rate of 5% , and the other yielding interest at the annual rate of 7%. Determine how much is invested in each account, if the total interest after one year is $855.

For problem #1, I'm thinking:

y=x+500

.04x+.06(500+x)=160

.04x+30+.06x=160

.10x+30=160

.10x=130

x=1300

y=1800

Anyone care to check my work and make comments? Sure would appreciate it.

Now the second problem is bothering me because I simply do not know where to start deriving information for my equation. I have found that these problems become relatively simple once I can get to the point where I solve for x. But, getting to that point has been a challenge. So far I drew a picture of two "account" boxes with a big 13,500 going into both of them....and that's all I got! I really need a push here so I can get going. Thanks for your time.
 
\(\displaystyle 1) \ \ Principal \ \ \ \ X \ \ \ Interest \ \ \ = \ \ Amt. \ Earned\)

\(\displaystyle \ \ \ \ \ \ \ \ \ x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .04 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .04x\)

\(\displaystyle (x+\$500) \ \ \ \ \ \ \ \ \ \ \ .06 \ \ \ \ \ \ \ \ \ \ \ \ \ \ .06(x+\$500)\)

\(\displaystyle Hence, \ .04x+.06(x+\$500) \ = \ \$160, \ implies \ x \ = \ \$1300, \ x+\$500 \ = \ \$1800.\)

\(\displaystyle 2) \ .05x+.07(\$13,500-x) \ = \ \$855\)
 
Justaguy,

it is \(\displaystyle \ \ Principal \times Interest \ \ RATE \times Time \ \ (in \ \ years) \ \ = \ \ Interest \ \ earned.\)

And a related one is \(\displaystyle \ \ Principal + Interest \ \ earned \ \ = \ \ Amount \ \ (final)\)
 
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