1/9 of the hats sold a local sport shop had laces.5/8 of the reminder were made of net.the rest of the hats were made of denim cloth .the shop had 81 denim hats .how many more net hats than denim hats did the shop have.
(1/9 + 5/8 * 8/9)x + 81 = x
First, let's find the total number of hats sold at the local sport shop. We know that 1/9 of the hats had laces, and the remaining hats were made of either net or denim.
So, 1/9 of the hats had laces, which means the remaining 8/9 of the hats were made of net or denim.
Let's determine the percentage of hats made of net. The problem states that 5/8 of the remaining hats were made of net, so we can calculate the percentage as follows:
8/9 * 5/8 = (8 * 5) / (9 * 8) = 40/72 = 5/9
So, 5/9 of the hats were made of net. This means that the remaining hats were made of denim.
We are given that there were 81 denim hats in the shop. Since the denim hats account for the rest of the hats (after considering the laced hats and net hats), we can calculate the total number of hats as follows:
Denim hats = Total hats - Laced hats - Net hats
81 = Total hats - 1/9 * Total hats - 5/9 * Total hats
81 = Total hats - (1/9 + 5/9) * Total hats
81 = Total hats - (6/9) * Total hats
81 = (9/9 - 6/9) * Total hats
81 = (3/9) * Total hats
We can solve this equation to find the total number of hats:
Total hats = 81 * (9/3) = 243
Now, let's find the number of net hats:
Net hats = Total hats * Percentage of net hats
Net hats = 243 * (5/9) = 135
Finally, we can calculate the difference between the number of net hats and denim hats:
Difference = Net hats - Denim hats
Difference = 135 - 81 = 54
Therefore, the shop has 54 more net hats than denim hats.
To solve this problem, let's break it down step by step:
1. Find the total number of hats sold in the shop:
- We are told that 1/9 of the hats had laces. This means that 1/9 + 5/8 of the hats were not made of denim cloth.
- The remaining (1 - 1/9 - 5/8) of the hats were made of denim cloth. This can be simplified as (72/72 - 8/72 - 45/72) = 9/72.
- Since 81 hats represent 9/72 of the total, we can find the total number of hats by multiplying 81 by the reciprocal of 9/72: (81 * 72/9) = 648 hats.
2. Find the number of net hats sold:
- We are told that 5/8 of the reminder (non-denim) hats were made of net material.
- To find the number of net hats, we multiply the total number of hats by 5/8: (648 * 5/8) = 405 hats.
3. Find the difference between the number of net hats and denim hats:
- We were also given that there were 81 denim hats.
- To find the difference, we subtract the number of denim hats from the number of net hats: (405 - 81) = 324.
Therefore, the shop had 324 more net hats than denim hats.