Question 113270: Helen Weller invested $15,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the total interest is equal to the interest on the two investments at the rate of 13%?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the additional money to be invested at 15% simple interest.
The interest earned on this amount can be expressed as: 0.15x
Now if we add that to the interest earned on the $15,000 invested at 12% simple interest, expressed as 0.12($15,000), then we have:
0.15x + 0.12($15,000)
The problem tells us that this amount is equal to the two investments (x + $15,000) at the rate of 13% (0.13). So now we can write the final equation:
0.15x + 0.12($15,000) = 0.13(x + $15,000) Now we simplify this and solve for x.
0.15x + $1,8000 = 0.13x + $1,950 Combining like-terms, we get:
0.02x = $150 and dividing by 0.02, we have:
x = $7,500
So $7,500 addtional must be invested.
Check: Let x = $7,500
0.15x + 0.12($15,000) = 0.13(x + $15,000)
0.15($7,500) + 0.12($15,000) = 0.13($7,500 + $15,000)
$1,125 + $1,800 = 0.13($22,500)
$2,925 = $2,925
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