The number of washers 3/32 inch thick that can be cut from a piece of stock 25 1/2 inches long, allowing 1/16 inch for waste for each cut is
(A) 160
(B) 163
(C) 260
(D) 272
(E) 408
not just answer, please tell me how to do it
each washer uses 3/32 + 1/16 = 5/32" of stock, including waste
(51/2) / (5/32) = 51/2 * 32/5 = 163.2
So, (B)
To solve this problem, we need to determine how many washers can be cut from a piece of stock with given dimensions, while accounting for the waste from each cut.
Let's break down the information given:
- The thickness of each washer: 3/32 inch
- Length of the stock: 25 1/2 inches
- Waste for each cut: 1/16 inch
To find the number of washers that can be cut, we must calculate the length occupied by each washer, including the wasted length.
1. Convert the stock length to a common fraction:
25 1/2 = (2 * 25 + 1) / 2 = 51/2 inches
2. Determine the length occupied by each washer:
Thickness of each washer = 3/32 inch
Waste for each cut = 1/16 inch (both sides of the washer)
Total length occupied by each washer = thickness + waste on both sides
= 3/32 + 1/16 + 1/16
= 3/32 + 2/32 + 2/32
= 7/32 inch
3. Calculate how many washers can be cut from the stock:
Number of washers = (Total length of the stock) / (Length per washer)
= (51/2) / (7/32)
= (51/2) * (32/7)
= 612/14
= 306/7
4. Simplify the fraction using division:
306 ÷ 7 = 43 remainder 5
= 43 + 5/7
≈ 43 5/7
Therefore, the number of washers that can be cut from the given stock length is approximately 43 5/7.
Now let's see which answer choice is closest to this result:
(A) 160
(B) 163
(C) 260
(D) 272
(E) 408
The closest answer choice is (B) 163.