Tom invested a total of $1400 in two accounts. One of the accounts pays 6% annual interest. The second account pays $10% annual interest. If Tom’s total interest for the year is $120, how much money did Tom invest in each of the accounts?
Answer: $500 at 6% and $900 at 10%
Explanation:
To solve this problem we set up two equations with two variables x and y and then we solve for each variable as follows:
Let x represent the amount invested at 6%
Let y represent the amount invested at 10%
x + y = 1400
0.06x + 0.10y = 120
In order to solve for one of the variables we must eliminate the other one. In this case if either the x or y coefficients in the first equation equaled the x and y in the second then we can subtract the equations. To accomplish this we will multiply the first equation by 0.1 and eliminate the y as follows:
0.10x + 0.10y = 140
0.06x + 0.10y = 120
When we subtract the two equations we end up with:
0.04x = 20
x = 20 / 0.04 = 500
Substituting 500 for x in the first equation we can now solve for y as follows:
500 + y = 1400
y = 1400 – 500 = 900
©Copyright 2007.Najwa S. Hirn. All rights reserved.
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