I have a math question I am stuck on. It is on the applications of linear systems. This is the question: A club raised 5000$ for a trip, they invested part of the money into a savings account with 4% interest, they put the rest of the money into a government bond with 3.5% interest. Overall they earned 190$ in interest in a year. How much was invested at each rate?

Question

I proceeded to create two equations, I made 2 variables which are x and y and these represent the unknown variables. The 2 equations I made are as followed:
x + y = 5000
0.04x + 0.035y = 190

I decided to use elimination to solve this problem so I multiplied the first equation by 3.5 and then I multiplied the bottom equation by 100 then the result is this:

3.5x + 3.5y = 17500
4x + 3.5y = 19000

I subtracted these two equations to get:
- 0.5x + 0y = -1500

So I divided both - 0.5x and -1500 by - 0.5 and got
x = 30000

But when I substitute 30000 for x in the first equation to find y I get -25000. I clearly did something wrong because the solutions for x and y don't add up to 5000. Could someone please help me understand where I went wrong and help give me the knowledge and tools to answer this question? It would be extremely appreciated!

Answer 1

misplaced decimal point in the last step

-1500 / -0.5 = 3000

Answer 2

Thank you so much R.Scott!! Very much appreciated, you've made my day.

Answer 3

When you divide 1500 by 0.5 you get 3000, not 30000
so in x+y = 5000, y = 2000

For your equations, I would have used substitution, using y = 5000-x from the first
then in the 2nd:
.03x + .035(5000-x) = 190
etc