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Question 786666: Suppose you invest $4,900 in stocks and bonds paying 7% and 3%, respectively. The interest from both investments after one year is $239. For the following problems, use x for the amount invested in stocks and y for the amount invested in bonds.
Write a mathematical expression for the total amount of money invested
I put 07y+.03x+239=4900 but it was wrong
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Sorry but it is wrong.
Let x = amount invested in stock paying 7%
Let y = amount invested in bonds paying 3%
The answer to "Write a mathematical expression for the total amount of money invested" is simply
(1) x + y
However, if the real question is to find out the amount of x and y, we need two equations, the total invested given by
(2) x + y = 4900 and the interest earned after one year given by
(3) 0.07x + 0.03y = 239
We must solve the system of equations given by (2) and (3).
I don't like to use decimals so I multiply both sides of (3) by 100 to get
(4) 7x + 3y = 23900
Now substitute
(5) x = 4900 - y from (2) into (4) to get
(6) 7*(4900 - y) + 3y = 23900 or
(7) 34300 - 7y + 3y = 23900 or
(8) 34300 - 4y = 23900 or
(9) -4y = 23900 - 34300 or
(10) 4y = 10400 or
(11) y = 10400/4 or
(12) y = 2600
And from (2) we get
(13) x = 4900 - 2600 or
(14) x = 2300
Let's check this with (3).
Is (0.07*2300 + 0.03*2600 = 239)?
Is (161 + 78 = 239)?
Is (239 = 239)? Yes
Answer to (possible) question: you invested $2300 in stock and $2600 in bonds.
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