Question

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?

Answer 1

small cup she sold = x = 98

large cup she sold = y =57

Answer 2

`\boxed {\boxed {\sf 98 \ Small \ Cups}}\\\\\boxed {\boxed {\sf 57 \ Large \ Cups}}`

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

• A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265.
• 1.25s+2.50g=265

Number

• A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155.
• s+g=155

Here is our system of equations:

`1.25s+2.50g=265 \\s+g=155`

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

• Subtract g from both sides of the equation.
• s+g=155
• s+g-g=155-g
• s=155-g

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

`1.25s +2.50g=265`

`1.25(155-g)+2.50g=265`

Distribute the 1.25

• 1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g

`193.75-1.25g+2.50g=265`

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

`193.75-1.25g+2.50g=265-193.75` (Subtract 193.75)

`-1.25g+2.50g=265-193.75`

`1.25g=71.25` (Combine like terms).

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

`1.25g/1.25=71.25/1.25\\g=71.25/1.25\\g=57`

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

`s+g=155`

`s+57=155`

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

`s+57-57=155-57\\s=155-57\\s=98`

Ashley sold 57 large cups and 98 small cups.