A shop had a number of T-shirts for sale. After selling 72 of them in the morning and 4/9 of the remainder in the afternoon, it was left with 1/3 of the T-shirts. How many T-shirts were sold altogether?

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To find the number of T-shirts sold altogether, we'll need to follow a step-by-step approach:

Step 1: Let's start by assigning a variable to represent the total number of T-shirts in the shop. Let's call it "x".

Step 2: The problem states that 72 T-shirts were sold in the morning. So, we need to subtract this number from the total number of T-shirts in the shop:
Total T-shirts after the morning sale = x - 72

Step 3: The problem further states that 4/9 of the remainder (after the morning sale) were sold in the afternoon. This means we need to find 4/9 of the "Total T-shirts after the morning sale". We can do this by multiplying it by 4/9:
T-shirts sold in the afternoon = (x - 72) * 4/9

Step 4: After the afternoon sale, the shop was left with 1/3 of the total T-shirts. Therefore, we need to multiply the original total number of T-shirts by 1/3 to find out how many were left:
T-shirts left = x * 1/3

Step 5: According to the problem, the number of T-shirts left equals the sum of the T-shirts sold in the morning and the T-shirts sold in the afternoon. So, we can set up an equation:
T-shirts left = 72 + (x - 72) * 4/9

Step 6: To solve the equation, we need to equate the expressions for T-shirts left:
x * 1/3 = 72 + (x - 72) * 4/9

Step 7: We can now solve this equation to find the value of x, which represents the total number of T-shirts in the shop.

Once we have the value of x, we can find the number of T-shirts sold altogether by subtracting the T-shirts left from the total number of T-shirts:
T-shirts sold altogether = x - T-shirts left

By following this step-by-step approach, we can determine the number of T-shirts sold altogether.