Question

At a summertime poolside snack bar, 200 ice cream scoops were sold in one day. Double scoops were sold for $1.25 each and single scoops were sold for $1 each. If the proceeds from the sale of the cones were $221.75, how many of each kinds of cone were sold? In all, how many scoops of ice cream were sold?

Answer 1

Answer: The number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.

Step-by-step explanation: Given that at a a summertime poolside snack bar, 200 ice cream scoops were sold in one day.

Double scoops were sold for $1.25 each and single scoops were sold for $1 each. The proceeds from the sale of the cones were $221.75.

We are to find the number of single scoop cones, double scoop cones and the number of scoops of ice cream that sold.

We Let x and y represents the number of cones of single scoop and double scoop ice cream that sold.

Then, according to the given information, we have

`x+y=200\\\\\Rightarrow x=200-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

and

`1* x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Comparing equations (i) and (ii), we get

`200-y=221.75-1.25y\\\\\Rightarrow 1.25y-y=221.75-200\\\\\Rightarrow 0.25y=21.75\\\\\Rightarrow y=(21.75)/(0.25)\\\\\Rightarrow y=87.`

From equation (i), we get

`x=200-87=113.`

Therefore, total number of scoops that were sold is

`113+2*87=113+174=287.`

Thus, the number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.

Answer 2

a) 87 double scoops and 113 single scoops.

b) 287 scoops of ice cream.

Explanation:

1. You need to make a system of equations, where double scoops are represented by
`x` and the single scoops are represented by
`y`:

`\left \{ {{x+y=200} \atop {1.25x+y=221.75}} \right.`

2. You can apply the Elimination Method:

- Multiply the first equation by -1 to cancel the variable
`y` from the system. Add both equations:

`0.25x=21.75`

- Solve for
`x`:

`x=(21.75)/(0.25)\\x=87`

- Substitute the value of
`x` into one of the original equations and solve for
`y`:

`87+y=200\\y=113`

3. You can calculate the total number of scoops of ice cream that where sold as below:

`2x+y`

4. Substitute values:

`2(87)+113=287` scoops of ice cream