Jordan and carson go to the movie theater and purchase refreshments for their friends. jordan spent a total of $25.75 on one bag of popcorn and three drinks. carson spoons a total of $81.25 on four bags of popcorn and nine drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink using these equations determine and state the price of a drink to the nearest cent

A bag is 4$, a drink is 7.25$.

Step-by-step explanation:

Let x be the price of a bag of popcorn and y the price of a drink.

After the notation, the system of equations is as follows:

x + 3y =25.75

4x + 9y = 81.25

Multiplying the first equation by 3, we obtain:

3x + 9y = 77.25

4x + 9y = 81.25

Substracting the first ecuation from the second, we obtain the following single equation:

x = 4.00 - the price of a popcorn bag is 4$

To find y, we introduce the now found x into the first equation:

4.00 + 3y = 25.75 ⇒ 3y = 21.75 ⇒ y =7.25 - the price of a drink is 7.25$

3/6   and 9/18

step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: