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%?

Question

22-07-2018
Mathematics

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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%?

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DeanR DeanR · Answer 1 · 2018-07-22T19:15:24+02:00

DeanR DeanR

22-07-2018

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 Link

AkhileshT AkhileshT · Answer 2 · 2019-09-09T08:07:42+02:00

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

Further explanation:

Given:

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

The student invested [tex]7\%[/tex] part of the money and rest at [tex]10\%[/tex].

At the end of year student receive [tex]\$\ 664[/tex] in interest.

Concept used:

The interest [tex]I[/tex] can be calculated as follows:

[tex]\boxed{I=p\cdot r\cdot t}[/tex]

Here, [tex]p[/tex] is the invested money, [tex]r[/tex] is the interest rate and [tex]t[/tex] is the time in years.

Calculation:

Consider [tex]x[/tex] as the money invested at [tex]7\%[/tex] of interest and rest money is invested at [tex]10\%[/tex] interest.

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

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

[tex]\boxed{7\%\text{ of }x+10\%\text{ of }(8200-x)=664}[/tex]

The percentage can be converted as follows:

[tex]0.07x+0.1(8200-x)=664[/tex]

Simplify the above equation to obtain the value of [tex]x[/tex] as follows:

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

Further simplify the above equation to obtain the value of [tex]x[/tex] as follows:

[tex]\begin{aligned}-0.03x&=-156\\0.03x&=156\\x&=\dfrac{156}{0.03}\\x&=5200\end{aligned}[/tex]

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

The amount of money invested at [tex]10\%[/tex] of interest is calculated as follows:

[tex]\boxed{8200-5200=3000}[/tex]

The amount of money invested at [tex]10\%[/tex] of interest is [tex]\$\ 3000[/tex].

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

Learn more:

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

2. Learn more about problem on interest rate https://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.