Beverly sells mangoes. She sold half her mangoes plus half a mango last Monday. Then she sold half her remaining mangoes plus a mango last tuesday. Again she sold half of her remaining mangoes plus half a mango on wednesday. She then sold the remaining mangoes on thursday. How many mangoes did beverly have at the beginning?
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This can not be solved without additional information.
Let's break down the information given step-by-step:
Step 1: On Monday, Beverly sold half of her mangoes plus half a mango.
Step 2: On Tuesday, she sold half of her remaining mangoes plus a mango.
Step 3: On Wednesday, she sold half of her remaining mangoes plus half a mango.
Step 4: On Thursday, she sold the remaining mangoes.
To find the initial number of mangoes Beverly had, we need to work backward:
1. On Thursday, Beverly sold the remaining mangoes. Therefore, let's call the remaining mangoes "x."
2. On Wednesday, Beverly sold half of her remaining mangoes plus half a mango. So, she had (x/2) - 0.5 mangoes remaining.
3. On Tuesday, she sold half of her remaining mangoes plus a mango. So, she had ((x/2) - 0.5)/2 - 1 = (x/4) - 0.75 mangoes remaining.
4. On Monday, she sold half of her mangoes plus half a mango. So, she had ((x/4) - 0.75)/2 - 0.5 = (x/8) - 0.875 mangoes remaining.
Since she had no mangoes remaining at the beginning, the equation becomes:
(x/8) - 0.875 = 0
Solving this equation will give us the answer.
(x/8) - 0.875 = 0
(x/8) = 0.875
x = 0.875 * 8
x = 7
Therefore, Beverly had 7 mangoes at the beginning.
To solve this problem, let's break it down step by step.
On Monday, Beverly sold half of her mangoes plus half a mango. Let's call the number of mangoes she had at the beginning as 'x'.
So, on Monday, she sold (x/2) + 0.5 mangoes.
After Monday's sales, Beverly had (x - (x/2) - 0.5) mangoes remaining.
On Tuesday, she sold half of her remaining mangoes plus one mango. Therefore, she sold ((x - (x/2) - 0.5)/2) + 1.
After Tuesday's sales, Beverly had [(x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1] mangoes remaining.
On Wednesday, she sold half of her remaining mangoes plus half a mango. This means she sold [((x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1)/2] + 0.5.
After Wednesday's sales, Beverly had [(x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1) - (((x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1)/2) - 0.5] mangoes remaining.
Finally, on Thursday, Beverly sold all of the remaining mangoes. So, she had [(x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1) - (((x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1)/2) - 0.5] - [(x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1) - (((x - (x/2) - 0.5) - ((x - (x/2) - 0.5)/2) - 1)/2) - 0.5] mangoes remaining.
Since she sold all the remaining mangoes, the quantity described above is equal to zero.
Now, you can solve the equation and find the value of 'x', which will represent the number of mangoes Beverly had at the beginning.