Question

Suppose a movie theater you work at sells popcorn in three different sizes. A small costs $2, a medium costs $5, a large costs $10. On your shift, you sold twice as many large containers as small ones. Write a system of equations for the situation. How many of each popcorn size did you sell?

Answer 1

Answer:

$\left \{ {{{s+m+l=250}} \atop {2s+5m+10l=1726 \atop {l=2s} \right.$

Small popcorns: 68

Medium popcorns:: 46

Large popcorns: 136

Step-by-step explanation:

The complete exercise is: "Suppose the movie theater you work at sells popcorn in three different sizes. A small costs $2, a medium costs $5, and a large costs $10. On your shift, you sold 250 total containers of popcorn and brought in $1726. You sold twice as many large containers as small ones. How many of each popcorn size did you sell?"

Let be "s" the number of small popcorns you sold,  "m" the number of medium popcorns syou sold and "l" the number of large popcorns you sold.

Set up a system of equations:

$\left \{ {{{s+m+l=250}} \atop {2s+5m+10l=1726 \atop {l=2s} \right.$

 To solve it:

- Multiply the first equation by -5 and add it to the second equation:

$\left \{ {{-5s-5m-5l=-1250}} \atop {2s+5m+10l=1726 \right. \\..................................\\-3s+5l=476$

- Substitute the third equation  into $-3s+5l=476$ and solve for "s":

$-3s+5(2s)=476\\\\7s=476\\\\s=68$

- Substitute this value into the third equation of the system to find "l":

$l=2(68)=136$

- Substitute the known values into the first equation of the system  and solve for "m" in order to find its value:

$68+m+136=250\\\\m=46$