Acollege 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%

$3000.

Step-by-step explanation:

Suppose the amount invested at 7% is $X and the amount invested at 10% is $Y (assuming that the college student invested all his/her income on the two schemes). Therefore:

X + Y = 8200 (The sum of investments is basically the total income).

0.07X + 0.1Y = 664 (The sum of the interest received from the invested amounts is actually the total return).

Now solving these 2 simultaneous equations:

x + y = 8200 (Equation 1)

7x + 10y = 66400 (Equation 2)

From (Equation 1):

x = 8200 - y (Equation 3)

Put (Equation 3) in (Equation 2):

7(8200 - y) + 10y = 66400.

57400 - 7y + 10y = 66400.

3y = 9000

y = 3000.

$Y is the amount invested at 10%, therefore the final answer is $3000!!!

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺