Alex, beth and carol share a sum of money. alex receives 0.7 of the sum of money. beth and carol receive the rest of the money. if beth receives 5/12 of the money shared by both her and carol, and carol receives $847, how much money does alex get?

Alex gets $3,388
.
Alex = 0.70 or 70% of total amount
Beth and Carol = 0.30 or 30% of total amount
Beth = 5/12 of the 30%
Carol = 7/12 of the 30%

Since Carol receives $847, the amount represents 7/12 of the 30%. To get the total 30% amount, divide $847 by 7/12

$847 ÷ 7/12 = $847 ÷ 0.5833333 = 1,452 the total 30%

Since 30% is equivalent to 1,452 we need to get the total or 100% amount to know the amount equivalent to 70% of total amount. Divide 1,452 by 30%

$1,452 ÷ 30% = $1,452 ÷ 0.30 = 4,840 total amount

Alex share is 0.70 or 70% of the total amount. Multiply 70% to 4,840.

4,840 * 70% = 3,388 Alex's share

But if 0.58 is used instead of 0.583333 then Alex's share would be: 3,407