Answer:
$17,500 was invested in the account that gained 10% and
$11,000 was invested in the account that lost 4%
Step-by-step explanation:
<u>Define the variables</u>:
- Let x be the money invested in the account that gained 10%.
- Let y be the money invested in the account that lost 4%.
<u>Given information:</u>
- $28,500 = total amount invested between the two accounts
- $1,310.00 = total amount gained
<u>Percentages in decimal form:</u>
Create a system of equations using the given information and defined variables:
![\begin{cases}x + y = 28500\\0.1x - 0.04y = 1310 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%20%2B%20y%20%3D%2028500%5C%5C0.1x%20-%200.04y%20%3D%201310%20%5Cend%7Bcases%7D)
<u>Rewrite</u> Equation 1 to make y the subject:
![\implies y=28500-x](https://tex.z-dn.net/?f=%5Cimplies%20y%3D28500-x)
<u>Substitute</u> into Equation 2 and <u>solve for x</u>:
![\implies 0.1x-0.04(28500-x)=1310](https://tex.z-dn.net/?f=%5Cimplies%200.1x-0.04%2828500-x%29%3D1310)
![\implies 0.1x-1140+0.04x=1310](https://tex.z-dn.net/?f=%5Cimplies%200.1x-1140%2B0.04x%3D1310)
![\implies 0.14x=2450](https://tex.z-dn.net/?f=%5Cimplies%200.14x%3D2450)
![\implies x=17500](https://tex.z-dn.net/?f=%5Cimplies%20x%3D17500)
<u>Substitute</u> the found value of x into Equation 1 and <u>solve for y</u>:
![\implies 17500+y=28500](https://tex.z-dn.net/?f=%5Cimplies%2017500%2By%3D28500)
![\implies y=11000](https://tex.z-dn.net/?f=%5Cimplies%20y%3D11000)
<u>Conclusion</u>
$17,500 was invested in the account that gained 10% and
$11,000 was invested in the account that lost 4%
Learn more about systems of equations here:
brainly.com/question/27930827