# How can I find the ages of the people in a word problem involving family ties which seems intricate?

The problem is as follows:

Marvin is the only son of Jennifer's grandfather, and Lindsey is the only daughter-in-law of Marvin's grandfather. If the only children of Jennifer are twins of 7 years of age and in this family it is true that from one generation to another consecutive 19 years have elapsed, what is the sum of the ages of the father and the great-grandfather of Jennifer?

The alternatives in my book are:

• $109$ years
• $135$ years
• $128$ years
• $116$ years
• $147$ years

Normally I would have tried to give an attempt to solve and show my progress but in this case I'm stuck at the very beginning hence I can't offer much other than what I'm already understanding which is described in the following lines.

I don't know if the way to go is to build up a single variable equation or is it a square one?.

The place where I'm stuck at is Lindsey, what kind of clue does she gives to the problem because I don't know how to relate it with the others.

Therefore, this problem has got me go around in circles for several days and I can't find how to get a clue where to begin. Can somebody help me to go in the right direction?.

It would help me the most if a suggested answer could include a visual aid to relate family ties. I mean how to tell in a tree where is the great grandfather, grandfather, son (husband) and daughter-in-law and grandchildren. To me this would greatly improve my understanding of this, since I'm lost at here where to tell the difference and understand how to make the math.

• There is a word missing from your question. "... how much do the ages of the father and the great-grandfather of Jennifer ...?" – N. F. Taussig Sep 10 '18 at 15:23
• @N.F.Taussig I've just edited the question. The word is sum. So it is asking how much is the sum of the ages from the father and the great-grandfather of Jennifer. – Chris Steinbeck Bell Sep 10 '18 at 15:24
• @MohammadZuhairKhan Interesting approach, although it does seem to play around with the given alternatives, perhaps could you develop a little bit more?. So I can get a grasp of what you meant, since in comments there isn't much space to show my doubts. Again this yet doesn't answer what kind of info does add Lindsey?. – Chris Steinbeck Bell Sep 10 '18 at 15:28
• Well the answer explained it before I could. – Mohammad Zuhair Khan Sep 10 '18 at 15:36

Following the suggestions from Ross. I'm posting this answer in case somebody encounters a similar situation.

It helps a lot to know who are the characters in this passage and the definitions therefore below is a list of what Merriam Webster say about each: (for purposes of brevity I omitted other entries in the dictionary and selected the ones to which applies to family ties)

Great-grandfather: the father of one's grandmother or grandfather.

Grandfather: the father of one's father or mother.

Father: a man who has begotten a child.

Daughter: a human female descendant. Another way to tell it, a female offspring especially of human parents.

Son: a human male descendant. Or a male offspring especially of human beings.

Child: an unborn or recently born person. A young person especially between infancy and youth

In-law: a relative by marriage.

Daughter-in-law: the wife of one's son or daughter.

From establishing these definitions we must know that the key is by whom we're setting a reference point. In this case is Jennifer, as the passage asks about her relatives from older generations.

From all of these I build up a vertical arrow from which we can see the time elapsed. This considers the clue that between one generation to another there is a gap of 19 years.

As it was mentioned, luckily we do not have to worry much about the information which does add Lindsey to the problem other than just a complementary one but it does not affect the ages of the family as she is not directly linked to Jennifer or Marvin's family in the sense that she is not affected by the "generation gap" which the problem mentions.

Therefore as shown all that is left to do is to move backwards in the arrow and sum up to the present time to get the ages.

From this is established that the sum of the ages of Jennifer's father and great-grandfather are:

$$83+45=128$$

which appears as one of the alternatives. Hence that would be the answer.

• This is what I was pointing at. Well done. – Ross Millikan Sep 12 '18 at 4:27

You don't have to worry about the sideways relationships in the tree, you just need to worry about the generations. Just make a line for each generation in the tree and write people's names in as you find out where they belong. Write Jennifer on one line. Her grandfather goes two lines above, then Marvin is his son, so he goes on the line in between. So far we have

• Jennifer's grandfather
• Marvin
• Jennifer

Now Lindsay goes on the line with Jennifer's grandfather, but doesn't matter to the question. Marvin's grandfather goes above, the twins below and our list is complete. Then the twins are $7$ and you add $19$ for each line up. We get Marvin is $45$, his grandfather is $83$, and the sum is $128$

• I'm trying to follow your directions about the line. Perhaps can you include this drawing in your answer so I can compare mine so what I'm understanding is the same as what you're trying to say?. – Chris Steinbeck Bell Sep 10 '18 at 15:34
• The lines are the lines of the table representing the generations. I included the table part way through where it has three lines. The completed one will have one more line above and one more below. – Ross Millikan Sep 10 '18 at 15:38
• @ChrisSteinbeckBell Marvin is Jennifer's father and Lindsey is her grandmother. Does it help? – Vasya Sep 10 '18 at 15:56
• @Vasya It does from looking at a diagram which I have included in a proposed answer. Thanks!. – Chris Steinbeck Bell Sep 12 '18 at 4:12
• @RossMillikan I've added an answer following your suggestions. Not yet sure if that was what you wanted to mean. The answer does check with yours. Hopefully I understood you right. – Chris Steinbeck Bell Sep 12 '18 at 4:15