Question

Elena invests a total of $70,000 in two different accounts for one year: some in a credit union at 5% interest, and the rest in a bank at 3% interest. if the investments earn$2,350 at the end of the year, how much money did elena invest in each account?

1. We want to know the amount of money invested in each account– in other words, we want to know the amount invested in the 5% account and the amount invested in the 3% account.
Each of the things we are trying to find will be represented by a variable:
x = amount invested at 5%
y = amount invested at 3%
Since we have two variables to solve for, we will need to find a system of two equations to solve.
We are given two numbers in the problem:
$70,000 = total money invested in both accounts$2,350 = total interest earned in both accounts
Let’s start with the $70,000. Elena wants to split this money into two parts. We have chosen to call the two parts x and y. Since these two parts must total to$700,000, this gives us our first equation:
x + y = 70,000
Now let’s look at the $2,350, the interest earned on the two accounts together. Let’s think about the formula for calculating simple interest : Interest = (Principle)(Rate)(Time) Since the time period in this problem is one year, our simple interest equation becomes: Interest = (Principle)(Rate)(1) or Interest = (Principle)(Rate) Each account has a different amount of money invested in it (either x dollars or y dollars), and each account has a different interest rate (either 5% or 3%). This gives us the following: Interest earned on x dollars = (x)(5%) = .05x and Interest earned on y dollars = (y)(3%) = .03y The total interest earned in both accounts is$700, so our second equation is:
Interest earned on x dollars + interest earned on y dollars = total interest
.05x + .03y = 2,350
If we multiply both sides of this equation by 100 to clear the decimals, it becomes:
5x + 3y = 23,500
Now we’ll solve the system of equations:
x + y = 70,000
5x + 3y = 23,500
Multiply the first equation by -3, then add the equations:
-3x – 3y = -210,000
5x + 3y = 23,500
x = – 93,250
Ann invested $– 93,250 in the account that pays 5% interest. To find the amount invested in the other account, substitute – 93,250 for x in either of our equations. We’ll choose the easier equation: x + y = 70,000 -93,250 + y = 70,000 y = 163,250 Ann invested$163,250 in the account that pays 3% interest.