Answer:
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.
