Respuesta :
Answer:
The system of equations are [tex]\left \{ {{2x+9y=71.75} \atop {12x+8y=143}} \right.[/tex]
The price of one drink is $7.75 and the price one bag of popcorn is $6.25.
Step-by-step explanation:
Let the cost of 1 drink be 'x'.
And also let the cost of 1 bag of popcorn be 'y'.
Now according to question,
Jaxon spends a total of $71.75 on 2 drinks and 9 bags of popcorn.
So framing in equation form, we get;
[tex]2x+9y=71.75\ \ \ \ \ equation\ 1[/tex]
Again, Robert spends a total of $ 143.00 on 12 drinks and 8 bags of popcorn.
So framing in equation form, we get;
[tex]12x+8y=143\ \ \ \ \ equation\ 2[/tex]
Multiplying equation 1 with 6 we get;
[tex]6(2x+9y)=6\times71.75\\\\12x+54y = 430.5[/tex]
Now Subtracting equation 2 from equation 1 we get;
[tex](12x+54y) -(12x+8y) = 430.5-143\\\\12x+54y-12x-8y= 287.5\\\\46y= 287.5\\\\y=\frac{287.5}{46}= \$6.25[/tex]
Now Substituting the value of y in equation 1 we get;
[tex]2x+9y=71.75\\\\2x+9\times6.25 =71.75\\\\2x+56.25=71.75\\\\2x=71.75-56.25\\\\2x=15.5\\\\x=\frac{15.5}{2} =\$7.75[/tex]
Hence The system of equations are [tex]\left \{ {{2x+9y=71.75} \atop {12x+8y=143}} \right.[/tex]
Also The price of one drink is $7.75 and the price one bag of popcorn is $6.25.
