8) 10 1/2 tonners of sand are to be shared between a number of builders. One of them receives 4/7 of the total and the remaining sand is shared by 3 builders. How much does the fourth builder receive and how much sand does each of the other 3 builders receive?
Answer (1)
To solve this problem, we first need to figure out how much sand each builder receives based on the fractions provided in the problem.
Determine the total quantity of sand in tons:
The total amount of sand is given as 10 1/2 tons. This can be converted to an improper fraction as follows:
10 2 1 = 2 21 tons
Calculate the amount received by the fourth builder (who receives 4/7 of the total):
Sand received by the fourth builder = 7 4 × 2 21
Let's perform the multiplication:
7 4 × 2 21 = 7 × 2 4 × 21 = 14 84 = 6 tons
So, the fourth builder receives 6 tons of sand.
Find the remaining sand to be shared by the other 3 builders:
Subtract the sand received by the fourth builder from the total sand:
2 21 − 6 = 2 21 − 2 12 = 2 9 tons
Calculate the amount each of the other 3 builders receives:
Since this remaining sand is equally shared among the 3 builders:
Sand received by each of the other 3 builders = 3 1 × 2 9 = 6 9 = 2 3 tons
Thus, each of the other 3 builders receives 1 2 1 tons or 2 3 tons.
Therefore, the fourth builder receives 6 tons of sand, and each of the other 3 builders receives 1 2 1 tons of sand.
