Question

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%.

Answer 1

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:

$\begin{cases}x + y = 28500\\0.1x - 0.04y = 1310 \end{cases}$

Rewrite Equation 1 to make y the subject:

$\implies y=28500-x$

Substitute into Equation 2 and solve for x:

$\implies 0.1x-0.04(28500-x)=1310$

$\implies 0.1x-1140+0.04x=1310$

$\implies 0.14x=2450$

$\implies x=17500$

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

$\implies 17500+y=28500$

$\implies y=11000$

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:

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