A grocer sells apples for $1.35 each, pears for $1.45 each and oranges for $1.60 each. She also offers a discount of 70c for anyone who buys two pieces of fruit, and a discount of $1.60 for anyone who buys three pieces of fruit. One day she sells 50 pieces of each type of fruit, for a total of $202. How many customers did she have, assuming each customer bought 1, 2 or 3 pieces of fruit?

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To solve this problem, we need to find the number of customers who bought 1, 2, or 3 pieces of fruit. Let's go step by step to find the solution.

Step 1: Calculate the total sales for each fruit type.
The grocer sold 50 pieces of each type of fruit, so the total sales for each fruit can be calculated as follows:
Total sales of apples = 50 * 1.35 = $67.50
Total sales of pears = 50 * 1.45 = $72.50
Total sales of oranges = 50 * 1.60 = $80.00

Step 2: Define the number of customers who bought three pieces of fruit.
Let's assume the number of customers who bought three pieces of fruit is "x".

Step 3: Calculate the discount for customers who bought two pieces of fruit.
The grocer offers a discount of $0.70 for customers who bought two pieces of fruit.

Step 4: Calculate the discount for customers who bought three pieces of fruit.
The grocer offers a discount of $1.60 for customers who bought three pieces of fruit.

Step 5: Set up the equation.
Using the information above, we can set up an equation to solve for "x":
67.50 + 72.50 + 80.00 - 1.60x - 0.70(50 - x) = 202

Let's solve the equation:
67.50 + 72.50 + 80.00 - 1.60x - 0.70(50 - x) = 202

Simplify the equation:
220.00 - 1.60x - 35 + 0.70x = 202

Combine like terms:
-0.90x + 185 = 202

Subtract 185 from both sides of the equation:
-0.90x = 17

Divide both sides of the equation by -0.90:
x = -17 / -0.90
x ≈ 18.89

Step 6: Interpret the solution.
Since we cannot have a fraction of a customer, we can conclude that the number of customers who bought three pieces of fruit is approximately 18.

Step 7: Calculate the number of customers who bought one or two pieces of fruit.
The total number of customers can be calculated by subtracting the number of customers who bought three pieces of fruit from the total number of fruit pieces sold:
Total number of customers = 50 - 18 ≈ 32

So, the grocer had approximately 32 customers, assuming each customer bought 1, 2, or 3 pieces of fruit.