The manager at a smoothie stand keeps track of the number of protein smoothies and berry smoothies sold each day and the total money received. On Wednesday, a total of 100 smoothies were sold, and the money collected was $836. If protein smoothies are sold for $10 and berry smoothies are sold for $6, how many protein smoothies and berry smoothies were sold?

Given:
Protein smoothie costs $10
Berry smoothie costs $6
Total smoothies sold  = 100
Total money collected = $836

Let
x = number of protein smoothies sold
y = number of berry smoothies sold

Then
x + y = 100           (1)
10x + 6y = 836     (2)

From (1), obtain
y = 100 - x            (3)

Substitute (3) into (2).
10x + 6(100 - x) = 836
4x + 600 = 836
4x = 236
x = 59
y = 100 - x = 41

Answer:
59 protein smoothies and 41  berry smoothies were sold.