We have to solve the problem without using algebra.

Question

Mimi's market sold 24 heads of lettuce one morning. That afternoon 2/7 of the remaining heads of lettuce were sold. The number of heads left was now 1/2 of the number the market had at the beginning of the day. How many heads of lettuce were there at the beginning of the day?

Answer 1

OK! so I played with it too! 

 

It is a trial and error process, but the key is that the afternoon is divided into 7ths. so you have to make it true until the rest 5/7 is 1/2 of the total.

 

So yes, start with 2 and 5, --> 5 cannot be 1/2 of total,  [2+5=7]

now try 4 and 10 --> 10 is still not 1/2 of total

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 :

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until you get to 16 and 40.

 

It is a trial and error -  I just always doubled it until the last number was 1/2 of the total.

Answer 2

Ana, I played with this problem and came up with an answer.  Since you have the remaining divided into sevenths, it makes sense that the remaining after selling 24 is a multiple of 7.  Keep adding 24 to multiples of 7 until you find your answer with the given information.