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Madison has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. Each small cup holds 12 ounces of lemonade and each large cup hold 22 ounces of lemonade. Madison used 1240 ounces of lemonade and sold 10 more large cups than small cups. Write a system of equations that could be used to determine the number of small cups sold and the number of large cups sold. Define the variables that you use to write the system.

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Answer:

[tex]12x+22(y+10)=1240, y=x[/tex]

small cups=30

large cups=40

Step-by-step explanation:

let x be the number of small cups and y the number of large cups.

-Given that 10 more cups than small cups of lemonade were sold:

[tex]12x+22(y+10)=1240[/tex]

#Before the 10 more were sold, the number of x and y sold were equal>

[tex]x=y\\\\\therefore 12x+22(x+10)=1240\\\\12x+22x+220=1240\\\\34x=1240-220\\\\34x=1020\\\\x=30[/tex]

The number of small cups sold was 30

#Since, the number of large cups was 10 more, y=x+10=30+10=40

The system of equations that can be used to determine the number of small cups sold and the number of large cups sold is:

12s + 22b = 1240

b - s = 10

Where:

s = number of small cups

b = number of big cups

The two equations are simultaneous equations. These equations have to solved jointly in order to determine the required values.

To learn more about simultaneous equations, please check: brainly.com/question/23589883

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