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So for this, we will be doing a system of equations, with one equation representing the total invested and the other equation representing the total gained from the investments. But first, we have to do calculations:
firstly, to represent a percentage gain (in this case 12% gain) you are to add 0.12 (12% in decimal form) to 1 to get 1.12. <em>Keep 1.12 in mind, as it will be used for the equations.</em>
Next, to represent a percentage loss (in this case 11%), you are to subtract 0.11 (11% in decimal form) from 1 to get 0.89. <em>Keep 0.89 in mind, as it will be used in the equations.</em>
Next, we need to find the total amount of money after the investments. To do this, add 21,000 and 1,715 together to get 22,715. <u>$22,715 is the total amount of money gained in 1 year.</u>
Now that we have all of our information, we can form our equations as such:
- Let x = $ invested into the account with 12% gain and y = $ invested into the account with 11% loss
Now with these system of equations, I will be using the substitution method. So firstly, with the first equation subtract x on both sides of that equation:
Now that we know that y = 21000 - x, replace y for (21000 - x) in the second equation and solve for x as such:
Now that we have the value of x, substitute it into either equation to solve for y:
<u>In short, $17500 was invested into the account that gained 12% and $3500 was invested into the account that had lossed 11%.</u>