contestada

Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?

$_______was invested in the account that gained 10% and
$_______ was invested in the account that lost 4%.

Respuesta :

semsee45

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:

Define the variables:

  • Let x be the money invested in the account that gained 10%.
  • Let y be the money invested in the account that lost 4%.

Given information:

  • $28,500 = total amount invested between the two accounts
  • $1,310.00 = total amount gained

Percentages in decimal form:

  • 10% = 0.1
  • 4% = 0.04

Create a system of equations using the given information and defined variables:

[tex]\begin{cases}x + y = 28500\\0.1x - 0.04y = 1310 \end{cases}[/tex]

Rewrite Equation 1 to make y the subject:

[tex]\implies y=28500-x[/tex]

Substitute into Equation 2 and solve for x:

[tex]\implies 0.1x-0.04(28500-x)=1310[/tex]

[tex]\implies 0.1x-1140+0.04x=1310[/tex]

[tex]\implies 0.14x=2450[/tex]

[tex]\implies x=17500[/tex]

Substitute the found value of x into Equation 1 and solve for y:

[tex]\implies 17500+y=28500[/tex]

[tex]\implies y=11000[/tex]

Conclusion

$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:

https://brainly.com/question/27930827

Otras preguntas