Question

at a concession stand 9 slices of pizza and 5 soft pretzels cost $33.25. If 4 slices of pizza and 6 soft pretzels cost $19.50. What is the cost of a soft pretzel?

Answer 1

The cost of soft pretzel is $1.25

Explanation:

Let $x be the price of one slice of pizza and $y be the price of one soft pretzel.

1. 9 slices of pizza cost $9x and 5 soft pretzels cost $5y. Together they cost $33.25, then

9x+5y=33.25.

2. 4 slices of pizza cost $4x and 6 soft pretzels cost $6y. Together they cost $19.50, then

4x+6y=19.50.

3. Solve the system of two equations:

`\left\{\begin{array}{l}9x+5y=33.25\\4x+6y=19.50\end{array}\right..`

Multiplythe first equation by 4, the second equation by 9 and subtract them:

`4(9x+5y)-9(4x+6y)=4\cdot 33.25-9\cdot 19.50,\\ \\36x+20y-35x-54y=133-175.5,\\ \\-34y=-42.5,\\ \\y=\$1.25.`

Then

`4x+6\cdot 1.25=19.50,\\ \\4x=19.50-7.50,\\ \\4x=12,\\ \\x=\$3.`

Answer 2

Answer: Each soft pretzel cost $1.25

Explanation:

Hi, we have to write an equation for each case:

9 x + 5 y = 33.25

4x +6 y = 19.50

Where x is the price of 1 slice of pizza, and y is the price of each soft pretzel.

Multiplying the first equation by 4, and the second equation by 9

36x +20y =133

36x +54y =175.5

And subtracting the first equation to the second equation

36x +54y =175.5

-

36x +20y =133

____________

34 y = 42.5

Solving for y

y =42.5/34

y = $1.25

Each soft pretzel cost $1.25