$5130 is to be divided equally among the members of a family group. Eight members of the family obtained knowledge of the loot and insisted their share.
Determine the original number of family members.
I don't want the answer just need to know the formula to work it out... or a similar question to this as an example
This is more a riddle than math.
In my opinion, it is hinged on the word "equally", which could mean equally to the dollar, or to the cent.
Taking the first case: everyone has an equal number of dollars.
Factoring 5130, we have as prime factors:
2,3³,5,19, which give rise to the following possible factors:
1,2,3,6,9,10,15,18,19,27,30,38,45,54,57,... up to 5130
So the original number of family members can be any of those numbers (factors).
If the family members are all sibblings born to the same mother, the maximum number is 69 (record set in the 18th century by a Russian family), see
http://www.guinnessworldrecords.com/world-records/3000/most-prolific-mother-ever
If divided to an equal number of cents, there will be even more possibilities.
To determine the original number of family members, you can use the formula:
Original Number of Family Members = Total Amount / Share per Member
In this case, the total amount is $5130 and there are eight members who insisted on their share. So, the formula becomes:
Original Number of Family Members = $5130 / 8
Simplifying it:
Original Number of Family Members = $641.25
However, it is not possible to have 641.25 family members because the number of family members must be a whole number. So, in this case, we would round down to the nearest whole number.
Thus, the original number of family members is 641.
To solve this problem, you can use a simple algebraic equation. Let's assume the original number of family members is represented by 'x'.
According to the problem, the $5130 is divided equally among the members of the family group. So, each member would receive an equal share, which can be calculated as $5130 divided by 'x'.
The equation becomes:
5130 / x = 8
Solving this equation will give you the value of 'x', which represents the original number of family members.
To solve this equation, you can multiply both sides of the equation by 'x':
5130 = 8x
Now, divide both sides of the equation by 8:
x = 5130/8
Performing that division would give you the value of 'x', which is the original number of family members.
A similar example could be:
A group of friends went out for dinner and the total bill was $160. If each friend paid an equal amount of money, and there were 5 friends in total, how much did each friend pay?
In this case, you would use the equation:
160 / x = 5
Solving this equation would give you the answer, with 'x' representing the amount each friend paid.