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.