Asked by Vanessa

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?

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!

Answers

Answered by R.scott
misplaced decimal point in the last step

-1500 / -0.5 = 3000
Answered by Vanessa
Thank you so much R.Scott!! Very much appreciated, you've made my day.
Answered by Reiny
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

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