By creating a system of equations and using substitution, we determined that 26 small smoothies and 20 large smoothies were sold to achieve a total of 46 smoothies and $234 in sales.
We are given a scenario where a total of $234 is collected from selling small and large smoothies. The problem states that the total number of smoothies sold is 46.
The price of a small smoothie is $4 and that of a large smoothie is $6.50. We can formulate a system of equations to solve for the number of small (s) and large (l) smoothies sold. Here are the equations based on the given information:
s + l = 46 (The total number of smoothies sold is 46.)
4s + 6.50l = 234 (The total sales from the smoothies amount to $234.)
To find the number of each size sold, we can use the method of substitution or elimination. Let's use substitution:
Solve the the first equation for s: s = 46 - l
Substitute this expression for s in the second equation: 4(46 - l) + 6.50l = 234
Simplify and solve for l: 184 - 4l + 6.50l = 234 ⇒ 2.50l = 50 ⇒ l = 20
Now, substitute l = 20 into the first equation to find s: s + 20 = 46 ⇒ s = 26
Therefore, 26 small smoothies and 20 large smoothies were sold.