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 fr…

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asked Apr 8, 2019 122k views

2 Answers

Obto · Answer 1 · 2019-04-10T06:29:56+0000

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.

Martin Kearn · Answer 2 · 2019-04-13T11:31:47+0000

Answer:

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
and the single scoops are represented by
:

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

2. You can apply the Elimination Method:

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

0.25x=21.75

- Solve for
:

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

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

$87+y=200\\y=113$

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