Question 4291: Juan pLast year, Juan won a radio station contest for $25,000. He put part in a saving account that paid 3% interest, and the rest in a mutual fund that paid a 25% dividend. If the return on his investments was $5,150, how much did he put in each investment?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! First: Assign the variables.
Let x = the amount invested in the savings account @ 3%
Let y = the amount invested in the mutual fund @ 25%
Second: Write the sytem of equations. Change the percents to their decimal equivalents. 3% = 0.03 25% = 0.25
0.03x + 0.25y = $5,150.00 Total interest earned.
x + y = $25,000.00 Total amount invested. Rewite as x = $25,000.00 - y and substitute for x in the first equation.
0.03($25,000.00 - y) + 0.25y = $5.150.00 Solve for y.
$750.00 - 0.03y + 0.25y = $5,150.00 Simplify.
$750.00 + 0.22y = $5,150.00 Subtract $750.00 from both sides.
0.22y = $4,400.00 Divide both sides by 0.22
y = $20,000.00 Now find x.
x = $25,000 - y
x = $25,000.00 - $20,000.00
x = $5,000.00
Juan invested $5,000.00 in the savings account @ 3% interest, and $20,000.00 in the mutual fund @ 25% interest.
Check: 0.03($5,000.00) + 0.25($20,000.00) = $150.00 + $5,000.00 = $5,150.00
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