2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each
type did she sell?

Step-by-step explanation:

Let's make a system of equations.

First, define the variables.

Let s= small cups and g= large cups

Next, make 2 equations. 1 for the money and 1 for the number of cups.

Money

Number

Here is our system of equations:

Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.

Now we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.

Distribute the 1.25

Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.

      (Subtract 193.75)

     (Combine like terms).

1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25

Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.

Subtract 57 from both sides of the equation to isolate the variable, s.

Ashley sold 57 large cups and 98 small cups.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x