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 is 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? "I'm in 5th grade so don't use x as a part of the solution."

well, I am sorry but I just plain have to use algebra

had n at the start

sold 24 so have n-24 at noon

sold 2/7 of (n-24) and have n/2
so
n -24 - (2/7)(n-24) = n/2

14 n - 336 - 4 n + 96 = 7 n

3 n = 240

n = 80
----------------------------
check
n = 80
sold 24 so have 56
sold (2/7)56 = sold 16
so have 56 - 16 = 40
sure enough that is half of 80

Now if you can do that without algebra, well done :)

80

Why did the lettuce go to school? To get a little "head"ucation! Okay, let's figure this out together.

We know that Mimi's market sold 24 heads of lettuce in the morning. Let's say they started with x heads of lettuce at the beginning of the day.

After selling 24 heads in the morning, they still had x - 24 heads left.

Then, in the afternoon, 2/7 of the remaining heads were sold. This means (2/7) * (x - 24) heads were sold.

So after the afternoon sales, they still had (x - 24) - (2/7) * (x - 24) heads of lettuce left.

And we also know that this remaining amount is now 1/2 of the number of heads they had at the beginning of the day.

So, we can set up the equation: (x - 24) - (2/7) * (x - 24) = (1/2) * x

Now, to avoid using x, let's use a substitute. How about we use the letter "L" for lettuce? Okay, let's rewrite the equation:

(L - 24) - (2/7) * (L - 24) = (1/2) * L

Solving this equation will give us the number of heads of lettuce they had at the beginning of the day. Remember, L represents the total number of heads of lettuce.

To solve this problem, let's break it down step by step.

Step 1: Let's start by figuring out how many heads of lettuce were sold in the afternoon. The problem states that 2/7 of the remaining heads were sold. This means that the number of heads sold is (2/7) * (remaining heads).

Step 2: Now, let's determine the remaining heads of lettuce after the afternoon sale. We know that the remaining heads are 1/2 of the number at the beginning of the day. So, if x is the number of heads at the beginning of the day, the remaining heads are (1/2) * x.

Step 3: Combining the information from steps 1 and 2, we can write the equation: x - [(2/7) * (1/2) * x] = 24.

Step 4: Simplifying the equation, we get x - (1/7) * x = 24.

Step 5: Continuing to simplify, we have (7/7) * x - (1/7) * x = 24.

Step 6: Further simplifying, we get (6/7) * x = 24.

Step 7: Multiplying both sides of the equation by 7/6 to isolate x, we have x = (24 * 7/6).

Step 8: Calculating x, we find that x = 28.

Therefore, there were 28 heads of lettuce at the beginning of the day.

Catherine, Please show your work.

Damon, from (n-24) - (2/7)(n-24)=n/2, how did you get "14?" What made you decide to multiple each side by 14?