SOLUTION: Linda smaoke invests a total of $10,000 in two saving accounts. One account pays 7% invest, and the other, 8%. Find the amount placed in each account if the accounts receive a tota

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Question 1118658: Linda smaoke invests a total of $10,000 in two saving accounts. One account pays 7% invest, and the other, 8%. Find the amount placed in each account if the accounts receive a total of $710 in interest after 1 year.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=10000%2C0.07x%2B0.08y=710%29


7x%2B8y=71000
7x%2B8%2810000-x%29=71000-----simplify and solve this for x; and use to find y.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The algebraic solution shown by the other tutor is fine.

But if an algebraic solution is not required, there is a much easier and faster way to solve a problem like this.

If all the money is placed in the account that pays 7% interest, the interest for the year would be $700; if all is placed in the account that pays 8% interest, the interest for the year would be $800.

The ratio in which the money is split between the two investments is exactly related to where the actual interest of $710 lies between those two figures of $700 and $800.

Specifically, here is all you need to do to find the solution from here:

$710 is 1/10 of the way from $700 to $800; that means 1/10 of the money is invested at the higher rate.

1/10 of $10,000 is $1000; so $1000 at 8% and the other $9000 at 7%.