Respuesta :
Answer:
The system of equation used to find the cost of each drink and each popcorn bag are [tex]\left \{ {{3x+4y=24.25} \atop {9x+y=37}} \right.[/tex].
The price of each Popcorn bag is $3.25.
Step-by-step 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;
[tex]3x+4y=24.25[/tex] ⇒ 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;
[tex]9x+y=37.00[/tex] ⇒ equation 2
Hence The system of equation used to find the cost of each drink and each popcorn bag are [tex]\left \{ {{3x+4y=24.25} \atop {9x+y=37}} \right.[/tex].
On solving the above equations we get;
Multiplying equation 1 by 3 we get;
[tex]3(3x+4y)=24.25\times3[/tex]
[tex]9x+12y=72.75[/tex] ⇒ equation 3
Subtracting equation 2 from we get;
[tex]9x+12y-(9x+y)=72.75-37\\\\9x+12y-9x-y=35.75\\\\11y=35.75[/tex]
Dividing both side by 11.
[tex]\frac{11y}{11}=\frac{35.75}{11}\\\\y=\$3.25[/tex]
Substituting the value of y in equation 2 we get;
[tex]9x+y=37\\\\9x+3.25=37\\\\9x=37-3.25\\\\9x=33.75\\\\x=\frac{33.75}{9}\\\\x=\$3.75[/tex]
Hence The price of each Popcorn bag is $3.25.
