Samantha went to a concession stand and bought three pretzels and four sodas and paid a total of $11.25 for them. Raza went to the same stand and bought five pretzels and two sodas and paid a total of $8.25. (a) Could pretzels have cost $1.75 each and sodas $1.50 each? How can you evaluate based on the information given?

The answer is NO because based on the information given, Pretzels will cost $0.75 each and Sodas will cost $2.25 each

Step-by-step explanation:

Let x represent the cost of one pretzel

Let y represent the cost of one soda

According to the question, Samantha bought three pretzels and four sodas and paid a total of $11.25. Mathematically, this means:

3x + 4y = $11.25 eqn1

Raza also bought five pretzels and two sodas and paid a total of $8.25. Mathematically, this means:

5x + 2y = $8.25 eqn2

We solve both equations simultaneously using elimination method

3x + 4y = $11.25

5x + 2y = $8.25

We multiply eqn 1 and 2 by 5 and 3 respectively in order to eliminate variable x;

5 × 3x + 4y = 11.25

3 × 5x + 2y = 8.25

We have;

15x + 20y = 56.25 eqn3

15x + 6y = 24.75 eqn 4

We subtract eqn4 from eqn3:

14y = 31.5

y = 31.5/14

y= 2.25

If y=2.25, we substitute the value of y into eqn 1

3x + 4y = 11.25

3x + 4(2.25) = 11.25

3x + 9 = 11.25

3x = 11.25 - 9

3x = 2.25

x = 2.25/3

x = 0.75

Since x=0.75 and y=2.25, this means that the cost of one pretzel and soda is $0.75 and $2.25 respectively.

This renders the estimated cost of each item in the question false.

step-by-step explanation:

it's 15

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: