Question 1133346
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The traditional algebraic approach: 7% of amount x, plus 8% of amount ($57,500-x), equals $4245:<br>
{{{.07x+.80(57500-x) = 4245}}}<br>
Solve using basic algebra, although the decimals make for some ugly computations.<br>
I leave it to you to finish the problem by that method.<br>
An alternative method, based on finding where the actual interest of 4245 lies between the two amounts if all $57,500 had been invested in either one of the two accounts....<br>
$57,500 at 7% = 4025
$57,500 at 8% = 4600<br>
Find where the actual amount of interest lies between those two amounts:
The difference between those two amounts is $575.
The difference between the actual amount of interest and the amount of interest at 7% is $4245-$4025 = $220. <br>
So the amount of actual interest is 220/575 of the way from 7% to 8%; that means 220/575 of the total was invested at the higher rate of 8%.  Since the total amount was $57,500, the amount invested at 8% was $22,000; that means the amount invested at 7% was $57,500-$22,000 = $35,500.<br>
ANSWER: $35,500 at 7%; $22,000 at 8%<br>
Of course that is the answer you should get by solving the problem by the algebraic method.