Question

Scarlett has set up a lemonade stand outside her house and sells small cups and large

cups of lemonade. Each small cup holds 10 ounces of lemonade and each large cup
hold 20 ounces of lemonade. Scarlett sold 70 cups of lemonade totaling 1000 ounces.
Determine the number of small cups sold and the number of large cups sold.

Answer 1

Answer: 40 small cups sold and 30 large cups sold.

Explanation:

Let be "s" the number of small cups sold and "l" the number of large cups sold.

Based on the information given in the exercise, you can set up the following system of equations:

`\left \{ {{s+l=70} \atop {10s+20l=1000 }} \right.`

You can use the Elimination Method to solve the system of equations:

1. Multiply the first equation by -10.

2. Add both equations.

3. Solve for "l".

Then, you get:

`\left \{ {{-10s-10l=-700} \atop {10s+20l=1000 }} \right.\\.........................\\10l=300\\\\l=(300)/(10)\\\\l=30`

4. Finally, substitute the value of "l" into any original equation and solve for the variable "s" in order to find its value.

This is:

`s+30=70\\\\s=70-30\\\\s=40`