Question

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?

Answer 1

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

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.

Answer 2

No, because their respective prices are $0.75 and $2.25

Explanation:

Let's assume that the price of each pretzels is x and the price of each soda is y

3x + 4y = 11.25_____ equation 1

5x + 2y = 8.25_____ equation 2

Multiply equation 2 by the figure 2 so as to have both equation sharing the same coefficient of y

10x + 4y = 16.5____ equation 1

3x + 4y = 11.25____ equation 2

Now subtract equation 2 from 1

7x = 5.25

X = 5.25/7

X = 0.75

Now substitute x = 0.75 in equation 1

10x + 4y = 16.5

10(0.75) + 4y = 16.5

7.5 + 4y = 16.5

4y = 16.5 - 7.5

4y = 9

Y = 2.25

Therefore,the cost of each pretzels is $0.75 while that of soda is $2.25