Answer:
Hi, there--
THE PROBLEM:
We invested $10,000 in 2 bank accounts. One account earns 14% per year the other earns 8%
per year. How much did we invest into each account if after the first year, the combined
interest from the 2 accounts is $1238?
A SOLUTION:
Define Variables:
Let x be the amount you originally invested in the first account.
Let y be the amount you originally invested in the second account.
Write Expressions and Equations:
Since you invested a total of $10,00 in two accounts. An equation that represents this is
x + y = 10000
One account (say the first one) earns 14% per year. Recall that the decimal form of 14% is
0.14. An expression for the amount of interest you earn after the first year in this account is
0.14x.
The other account earns 8% per year. The decimal representation of 8% is 0.08. The amount
of interest you earn after one year in this account is 0.08y.
The combine interest from both account after one year is $1238. An equation representing
the total interest earned is
0.14x + 0.08y = 1238
Now we have a system of two equations with two variables. We can solve for x and y. Rewrite
the first equation in "y=" form.
x + y = 10000
y = 10000 - x
Substitute 10000-x for y in the second equation.
0.14x + 0.08y = 1238
0.14x + 0.08(10000 - x) = 1238
Solve this equation for x. Use the Distributive Property to clear parentheses.
0.14x + 800 - 0.08x = 1238
Combine like terms (0.14x-0.08x is 0.06x).
0.06x + 800 = 1238
Subtract 800 to both sides to isolate x on the left.
0.06x = 1238 - 800
0.06x = 438
Divide both sides of the equation by 0.06.
x = 438/0.06
x = 7300
In the context of this problem, x=7300 means that you invested $7300 in the first account.
Since you invested a total of $10000, you invested 10000-7300=$2700 in the second account.
Check your work by verifying that these amounts will yield the correct amount of interest.
Substitute 7300 for x and 2700 for y in the interest equation.
0.14x + 0.08y = 1238
0.14(7300) + 0.08(2700) = 1238
1022 + 216 = 1238
1238 = 1238
Check!
Hope this helps! Feel free to email if you have any questions about the
