invested $5000 in two accounts on at 5% and one at & 7% interests how much did I invest in each account to earn $310 in interest?

Question

 Invested $5,000 two accounts

one at 5%

one at 7%

how much did I invest in each account to earn $310 in interest?

Answer 1

The $5000 is split over two accounts. Let's say the amount in the first account is x and the amount in the second account is y. Thus,

 

5000 = x + y

 

We assume each of these accounts accumulates interest once, so that:

 

5310 = 1.05x + 1.07y

 

The above two equations should both be satisfied by the correct pair of x and y. There are multiple standard techniques for solving systems of equations. We can first solve for x in terms of y from the first equation (isolate x on left-hand side of equation).

 

x = 5000 - y

 

Substitute the right-hand side of the above equation for x in the second equation.

 

5310 = 1.05(5000 - y) + 1.07y

 

Distribute.

5310 = 5250 - 1.05y + 1.07y

 

Subtract 5250 from both sides of the equation. Combine like terms.

 

60 =  0.02y

 

Divide both sides of equation by 0.02.

 

3000 = y

 

Return to first equation to get x = 2000.

 

Thus, $2000 was invested at %5 interest and $3000 was invested at %7 interest.

 

We can check our answer.

 

5310 =?= 1.05(2000) + 1.07(3000)

5310 =?= 2100 + 3210

5310 =√= 5310

 

Yay!

Answer 2

Good morning, Josie. Let's call the 5% account amount x and the other y.

 

x + y = 5000

.05x + .07y = 310

 

First, we need to "solve the first equation for either x or y. Let's do x.

 

x = 5000 - y

 

Now, we are going to substitute this "value" for x into the 2nd equation.

 

.05(5000 - y) + .07y = 310

250 - .05y + .07y = 310

.02y = 60

y = 3000

 

Since x = 5000 - y, x = 2000

 

Hope this helps!