Algebra word problem

Question

Sam won 30,000 on a trip to Las Vegas. He invested some at 5% and the rest at 3%. At the end of the year he earned 1340 in interest. How much did he invest at each amount?

Answer 1

Hey Robert.

 

I'm assuming this question regards simple interest and not compounding interest. If it's compounding then your math is going to be a lot more painful.

 

Let's take a look at simple interest.

 

I = P*R*T

 

I = interest earned.

P = principal invested.

R = rate of return.

T = time.

 

Your question says Sam invested some of his 30,000 in a 5% account and the rest in a 3% account. Let's call some variables to set up our equation.

 

Pa = principal invested in the 3% account

Pb = principal invested in the 5% account

 

t will just be 1, since the time passed has been 1 year.

 

Ia = Pa*0.03*1

Ib = Pb*0.05*1

 

Right now we have 2 equations and 4 unknowns. Not good. What else do we know?

 

The total interest he made was $1340. That tells us:

 

Ia + Ib = $1340

 

We also know the grand amount he invested was $30,000. That tells us:

 

Pa + Pb = $30,000

 

Now we have our 4 equations:

 

Ia = Pa*0.03
Ib = Pb*0.05

Ia + Ib = $1340

Pa + Pb = $30,000

 

Let's add the first two equations.

 

Ia + Ib = Pa*0.03 + Pb*0.05

 

But according to equation 3, Ia + Ib = 1340.

 

1340 = Pa*0.03 + Pb*0.05

 

We can solve for Pa in terms of Pb from equation 4 and then substitute.

 

Pa = 30000 - Pb

 

1340 = (30000 - Pb)*0.03 + Pb*0.05

 

1340 = 900- 0.03*Pb + 0.05*Pb

 

440 = 0.02Pb

 

Pb = 22,000

 

Since Pa = 30,000 - Pb, we know that

 

Pa = 8,000.

 

So Sam invested 22,000 into a 5% account and 8,000 into a 3% account. It's always good to check your answers.

 

The sum of each individual principal should be 30,000

 

Pa = 22,000

Pb = 8,000

 

22,000 + 8,000 = 30,000. Check.

 

The sum of each individual interest should equal 1340.

 

Ia = 8000*0.03 = 240

Ib = 22000*0.05 = 1100

 

1100 + 240 = 1340. Checkmate.

 

Hope this helps.