Word Problem Question

Question

An estate valued at $650,000 is to be distributed among the wife, 3 children and 4 grandchildren. The children will each receive two times as much as each grandchild, and the wife will receive five times as much as each child. How much will the wife receive?

Answer 1

First, let's define the variables. Let c be the amount each child gets, g be the amount each grandchild gets, and w be the amount the wife gets.

If we take the word problem literally, it says the children (that means all 3 of them) will get twice as much as each grandchild. That means each 3c = 2g or g = 3/2c.

The wife gets five times as much as each child so w = 5c.

The total amount is divided up so: 3c + 4g + w = 650,000. Substituting 3/2c for g and 5c for w, we get:

3c + 4(3/2c) + 5c = 650,000

3c + 6c + 5c = 650,000

14c = 650,000

c = 46,428.57

Then g = 3/2c so g = 69,642.86

Then w = 5c so w = 232,142.86