Mr Hash bought some plates at a yard sale. After arriving home he found that 2/3 of the plates were chipped, 1/2 were cracked, 1/4 were both chipped and cracked only 2 plates were w/o chips or cracks. How many plates did he buy in all?
To find the total number of plates Mr. Hash bought, we can start by using the information given in the problem.
Let's assume the number of plates Mr. Hash bought is 'x'.
From the problem, we know that 2/3 of the plates were chipped. So, we can calculate the number of chipped plates as (2/3) * x.
Similarly, 1/2 of the plates were cracked. Therefore, the number of cracked plates would be (1/2) * x.
Since 1/4 of the plates were both chipped and cracked, we can calculate the number of plates that were both chipped and cracked as (1/4) * x.
Now, we have the following information:
Number of plates without chips or cracks = 2
Number of chipped plates = (2/3) * x
Number of cracked plates = (1/2) * x
Number of plates both chipped and cracked = (1/4) * x
From the problem, we know that the total number of plates Mr. Hash bought is equal to the sum of plates without chips or cracks, chipped plates, cracked plates, and plates both chipped and cracked.
Therefore, we can set up the equation:
2 + (2/3) * x + (1/2) * x + (1/4) * x = x
Now, we can solve the equation to find the value of x.
Multiply through by 12 to eliminate the denominators:
24 + 8x + 6x + 3x = 12x
24 + 17x = 12x
24 = -5x
Divide through by -5:
x = -24/5
However, it doesn't make sense to have a negative number of plates. So, there seems to be an error in the problem statement. Please double-check the information provided.