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?

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luisejr77 luisejr77 · Answer 1 · 2019-11-02T17:43:54+01:00

Answer:

[tex]\left \{ {{{s+m+l=250}} \atop {2s+5m+10l=1726 \atop {l=2s} \right.[/tex]

Small popcorns: 68

Medium popcorns:: 46

Large popcorns: 136

Step-by-step explanation:

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:

[tex]\left \{ {{{s+m+l=250}} \atop {2s+5m+10l=1726 \atop {l=2s} \right.[/tex]

To solve it:

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

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

- Substitute the third equation into [tex]-3s+5l=476[/tex] and solve for "s":

[tex]-3s+5(2s)=476\\\\7s=476\\\\s=68[/tex]

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

[tex]l=2(68)=136[/tex]

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

[tex]68+m+136=250\\\\m=46[/tex]