Question

Brianna spends a total of $24.25 on 3 drinks and 4 bags of popcorn. Chloe spends a total of $37.00 on 9 drinks and 1 bag of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations determine and state the price of a bag of popcorn to the nearest cent.

Answer 1

The system of equation used to find the cost of each drink and each popcorn bag are
`\left \{ {{3x+4y=24.25} \atop {9x+y=37}} \right.`.

The price of each Popcorn bag is $3.25.

Explanation:

Let the cost of each drink bag be 'x'.

Let the cost of each popcorn bag be 'y'.

Solution:

Now Given:

Brianna spends a total of $24.25 on 3 drinks and 4 bags of popcorn.

So we can say that;

Total money spend by Brianna is equal to 3 multiplied by cost of each drink plus 4 multiplied by cost of each popcorn bag.

framing in equation form we get;

`3x+4y=24.25` ⇒ equation 1

Also Given:

Chloe spends a total of $37.00 on 9 drinks and 1 bag of popcorn.

So we can say that;

Total money spend by Chloe is equal to 9 multiplied by cost of each drink plus 1 multiplied by cost of each popcorn bag.

framing in equation form we get;

`9x+y=37.00` ⇒ equation 2

Hence The system of equation used to find the cost of each drink and each popcorn bag are
`\left \{ {{3x+4y=24.25} \atop {9x+y=37}} \right.`.

On solving the above equations we get;

Multiplying equation 1 by 3 we get;

`3(3x+4y)=24.25*3`

`9x+12y=72.75` ⇒ equation 3

Subtracting equation 2 from we get;

`9x+12y-(9x+y)=72.75-37\\\\9x+12y-9x-y=35.75\\\\11y=35.75`

Dividing both side by 11.

`(11y)/(11)=(35.75)/(11)\\\\y=\$3.25`

Substituting the value of y in equation 2 we get;

`9x+y=37\\\\9x+3.25=37\\\\9x=37-3.25\\\\9x=33.75\\\\x=(33.75)/(9)\\\\x=\$3.75`

Hence The price of each Popcorn bag is $3.25.