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:

a) 87 double scoops and 113 single scoops.

b) 287 scoops of ice cream.

Step-by-step 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 $x$:

$x=\frac{21.75}{0.25}\\x=87$

- 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

Answer 2

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

$1\times x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

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

$200-y=221.75-1.25y\\\\\Rightarrow 1.25y-y=221.75-200\\\\\Rightarrow 0.25y=21.75\\\\\Rightarrow y=\dfrac{21.75}{0.25}\\\\\Rightarrow y=87.$

From equation (i), we get

$x=200-87=113.$

Therefore, total number of scoops that were sold is

$113+2\times87=113+174=287.$

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.