ireneportillo1211
Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Helene invested a total of $1,000 in two simple-interest bank accounts. One account paid 5% annual interest; the other paid 8% annual interest. The total amount of interest she earned after 1 year was $65. Find the amount invested in each account.

Sagot :

a  =  total amount invested at 5%

b = total amount invested at 8%

we know 5% was earned in interest from "a", so that'd be (5/100) * a or 0.05a.

we know 8% was earned in interest from "b", so that'd be (8/100) * a or 0.08b.

we also know that the total for both is 1000, a + b = 100.

[tex]\begin{cases} a + b = 1000\\ 0.05a+0.08b=65 \end{cases}\qquad \qquad \stackrel{\textit{since we know}}{a+b=1000}\implies b = 1000-a \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.05a+0.08(100-a)=65}\implies 0.05a+80-0.08a=65 \\\\\\ -0.03a+80=65\implies -0.03a=-15\implies a=\cfrac{-15}{-0.03}\implies \boxed{a = 500} \\\\\\ \stackrel{\textit{we know that}}{b = 1000-a}\implies b=1000-500\implies \boxed{b = 500}[/tex]

Step-by-step explanation:

Let  [tex]\textbf{\textit{x}}[/tex] be the amount invested into the account with a 5% annual interest and [tex]\textit{\textbf{y}}[/tex] be the amount invested into the account with an 8% annual interest,

It is stated that Helene invested a total of $1000, which can be written mathematically as

                                         [tex]x \ + \ y \ = \ 1000 \ \ \ \text{----- \ (1)}[/tex]  .

Subsequently, the total amount of interest after 1 year is $65. This statement can be changed into the equation below.

                                      [tex]0.05x \ + \ 0.08y \ = \ 65 \ \ \text{----- \ (2)}[/tex]  .

First, divide each term in equation (2) by 0.05, yields the expression

                                        [tex]x \ + \ 1.6y \ = \ 1300 \ \ \text{----- \ (3)}[/tex]   .

Then, let equation (1) be subtracted from equation (3) term-by-term,

                                [tex](x \ + \ 1.6y ) \ - \ (x \ + \ y) \ = \ 1300 \ - \ 1000 \\ \\ (x \ - \ x) \ + \ (1.6y \ - \ y) \ = \ 300 \\ \\ \-\hspace{3.15cm} 0.6y \ = \ 300 \\ \\ \-\hspace{3.38cm} \displaystyle\frac{3}{5}y \ = \ 300 \\ \\ \-\hspace{3.65cm} y \ = \ 500[/tex].

Therefore, the amount invested in each account is $500.

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.