Question

A college student earned $8200 during summer vacation working as a waiter in a restaurant on the boardwalk at the beach. The student invested part of the money at 7% and the rest at 10%. If the student received a total of $664 in interest at the end of the year, how much was invested at 10%?

Answer 1

Let f be the fraction invested at 10%. So (1-f) is the fraction at 7%. After one year the interest is

664 = 8200 f (.10) + 8200 (1-f) (.07) = 8200(.03)f + 8200(.07)

f = (664 - 8200(.07))/(8200(.03)) = .3659 = 36.59 %

Answer: 36.59%

Check:

8200(.3659)*.1 + 8200(1-.3659)*.07 = 664.01 good

Answer 2

The amount of money invested at $10\%$ of interest is $\boxed{\bf \ \ 3000}$.

Further explanation:

Given:

A college student is working as a waiter in a restaurant on a board walk at a beach and earned $\ \ 8200$ during summer vacation  

The student invested $7\%$ part of the money and rest at $10\%$.

At the end of year student receive $\ \ 664$ in interest.

Concept used:

The interest $I$ can be calculated as follows:

$\boxed{I=p\cdot r\cdot t}$  

Here, $p$ is the invested money, $r$ is the interest rate and $t$ is the time in years.

Calculation:

Consider $x$ as the money invested at $7\%$ of interest and rest money is invested at $10\%$ interest.

The amount of money invested at $10\%$ interest is $\ \ (8200-x)$.

The total interest amount for two accounts can be calculated as follows:

$\boxed{7\%\text{ of }x+10\%\text{ of }(8200-x)=664}$  

The percentage can be converted as follows:

$0.07x+0.1(8200-x)=664$  

Simplify the above equation to obtain the value of $x$ as follows:

$\begin{aligned}0.07x+0.1(8200-x)&=664\\0.07x+820-0.01x&=664\\-0.03x&=664-820\\-0.03x&=-156\end{aligned}$

Further simplify the above equation to obtain the value of $x$ as follows:

$\begin{aligned}-0.03x&=-156\\0.03x&=156\\x&=\dfrac{156}{0.03}\\x&=5200\end{aligned}$

From the above calculation it is concluded that the amount of money invested at $7\%$ of interest is $\ \ 5200$.

The amount of money invested at $10\%$ of interest is calculated as follows:

$\boxed{8200-5200=3000}$

The amount of money invested at $10\%$ of interest is  $\ \ 3000$.

Thus, the amount of money invested at $10\%$ of interest is $\boxed{\bf \ \ 3000}$.

Learn more:

1. Learn more about problem on percentage: brainly.com/question/1856923

2. Learn more about problem on interest rate brainly.com/question/3724002

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Simple interest

Keywords: Percentage, interest rate, money amount, invested, time, student, restaurant, beach, summer vacation, waiter.