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?

Answer 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.

Learn more about solving linear equations at : https://brainly.in/question/2582402

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