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. Keep 1.12 in mind, as it will be used for the equations.
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. Keep 0.89 in mind, as it will be used in the equations.
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. $22,715 is the total amount of money gained in 1 year.
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
[tex]x+y=21000\\1.12x+0.89y=22715[/tex]
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:
[tex]y=21000-x\\1.12x+0.89y=22715[/tex]
Now that we know that y = 21000 - x, replace y for (21000 - x) in the second equation and solve for x as such:
[tex]1.12x+0.89(21000-x)=22715\\1.12x+18690-0.89x=22715\\0.23x+18690=22715\\0.23x=4025\\x=17500[/tex]
Now that we have the value of x, substitute it into either equation to solve for y:
[tex]17500+y=21000\\y=3500\\\\1.12(17500)+0.89y=22715\\19600+0.89y=22715\\0.89y=3115\\y=3500[/tex]
In short, $17500 was invested into the account that gained 12% and $3500 was invested into the account that had lossed 11%.
