Algebra 2 college question homework

Question

Laura borrowed a total of $26,000 from two different banks to start a business. One bank charged the equivalent of 3% simple interest, and the other charged 4.5% interest. If the total interest after 1 year was $840, determine the amount borrowed from each bank.

Let x represent the principal on the business loan at 3%

Then, [ ] is the remaining amount borrowed at 4.5%

Answer 1

While I'm sure you no longer need help on this particular problem, I'll answer it for others' benefit...

First, in order to solve for two unknowns, you must have two equations. And in order to set up those equations it helps to define what each variable represents. You already stated that x is the principal on the loan at 3% interest. So I'll define y as the principal borrowed at 4.5%.

We know that the total borrowed was $26,000, so the first equation is easy: x + y = 26,000.

We also know that the total amount of simple interest after the first year is $840, so setting up the second equation is almost as easy. Think: how would you calculate the $$ AMOUNT of interest for each loan? I would multiply the interest rate (as a decimal) by the principal loan amount. So the $$ amount of interest for the first loan would be found by 0.03x, and the same for the second loan amount is 0.045y. To get the TOTAL $$ in interest, we would simply add the two, so the equation for the amount of interest is .03x + .045y = 840.

Now you have two equations, with your two variables identified. Simply use your preferred method (matrices, substitution, elimination, or graphing) to find the solution. I think either substitution or matrices would be simplest. Please let me know if you need help with any of these.

Be sure to check your solution by subbing your solution set (x,y) into each of your original equations. Both values must work both places for it to be correct.