A farmer has 120 bushels of for sale at a​ farmer's market. He sells an average of 14 5/8 bushels each day. After 5 ​days, what is the change in the total number of bushels the farmer has for sale at the​ farmer's market?

Write a signed number representing the change in the total number of bushels the farmer has for sale.
  
​(Type an​ integer, proper​ fraction, or mixed​ number.)

1 answer

To find the change in the total number of bushels the farmer has for sale, we need to subtract the number of bushels sold from the initial 120 bushels.
The farmer sells an average of 14 5/8 bushels each day, so after 5 days, he sells a total of 14 5/8 * 5 = 73 1/8 bushels.
Therefore, the change in the total number of bushels the farmer has for sale is 120 - 73 1/8.
To subtract mixed numbers, we need to make sure the fractions have the same denominator.
73 1/8 can be rewritten as 72 9/8.
120 - 72 9/8 = 120 - (72 * 8 + 9)/8 = 120 - (576 + 9)/8 = 120 - 585/8.
To subtract fractions, we need to find a common denominator, which in this case is 8.
120 - 585/8 = (120 * 8)/8 - 585/8 = 960/8 - 585/8 = (960 - 585)/8 = 375/8.
Therefore, the change in the total number of bushels the farmer has for sale is 375/8.
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