Okay, so the math club is having a bake sale, and they need to figure out their profit. Let me start by understanding the problem step by step. 

First, they sold three different types of baked goods: cookies, cupcakes, and brownies. Each type has different quantities sold and different prices. They also had a cost to bake all these items, which is $15. The question is asking for their profit, which I know is calculated by subtracting the total cost from the total revenue. 

Let me break it down. Profit = Total Revenue - Total Cost. So, I need to calculate the total revenue from each item, add them up, then subtract the $15 baking cost. 

Starting with the cookies. They sold 54 cookies, right? And the price is three for $1. Hmm, so every three cookies bring in $1. To find out how much money they made from cookies, I need to divide the total number of cookies by 3 and then multiply by $1. Let me check that. 

If they sold 54 cookies at three for a dollar, then 54 divided by 3 is 18. So that's 18 sets of three cookies, each set selling for $1. So 18 * $1 = $18. Got that part. 

Next, the cupcakes. They sold 20 cupcakes at $2 each. That seems straightforward. So 20 multiplied by $2. Let me compute that. 20 * 2 = $40. So they made $40 from cupcakes. 

Then the brownies. They sold 35 brownies at $1 each. Again, simple multiplication. 35 * $1 = $35. 

Now, adding up all the revenues from each item. So total revenue is $18 (cookies) + $40 (cupcakes) + $35 (brownies). Let me add those numbers. 18 + 40 is 58, and 58 + 35 is 93. So total revenue is $93. 

Then, subtract the total baking cost of $15. Profit = $93 - $15 = $78. 

Wait, let me double-check my calculations to make sure I didn't make a mistake. 

Starting with cookies: 54 divided by 3 is indeed 18, times $1 is $18. Correct. 

Cupcakes: 20 times $2 is $40. That's right. 

Brownies: 35 times $1 is $35. Correct. 

Adding them up: 18 + 40 is 58, plus 35. Let's see, 58 + 35. 50 + 30 is 80, and 8 + 5 is 13, so 80 + 13 is 93. That's right. 

Then subtract the cost: 93 - 15. 93 minus 10 is 83, minus 5 more is 78. So profit is $78. 

Hmm, that seems straightforward. Let me just make sure I didn't mix up any numbers. The quantities are 54, 20, 35. Prices for cookies are three for a dollar, so that's per three, not per one. The cupcakes are $2 each, brownies are $1 each. 

Another way to check: For cookies, 54 divided by 3 is 18 sets. Each set is $1, so 18 * 1 = $18. Correct. 

Cupcakes: 20 * 2 = 40. Correct. 

Brownies: 35 * 1 = 35. Correct. 

Total: 18 + 40 + 35 = 93. Then 93 - 15 = 78. 

Yes, that all adds up. I don't see any mistakes here. So the profit should be $78.
Therefore, the profit made by the math club from their bake sale is $\boxed{78}$ dollars.
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