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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?

Respuesta :

carlosego

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 [tex]x[/tex] and the single scoops are represented by [tex]y[/tex]:

[tex]\left \{ {{x+y=200} \atop {1.25x+y=221.75}} \right.[/tex]

2. You can apply the Elimination Method:

- Multiply the first equation by -1 to cancel the variable [tex]y[/tex] from the system. Add both equations:

[tex]0.25x=21.75[/tex]

- Solve for [tex]x[/tex]:

[tex]x=\frac{21.75}{0.25}\\x=87[/tex]

- Substitute the value of [tex]x[/tex] into one of the original equations and solve for [tex]y[/tex]:

[tex]87+y=200\\y=113[/tex]

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

[tex]2x+y[/tex]

4. Substitute values:

[tex]2(87)+113=287[/tex] scoops of ice cream

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

[tex]x+y=200\\\\\Rightarrow x=200-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]1\times x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

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

[tex]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.[/tex]

From equation (i), we get

[tex]x=200-87=113.[/tex]

Therefore, total number of scoops that were sold is

[tex]113+2\times87=113+174=287.[/tex]

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.

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