Question

Look at the graph and picture and answer these questions (please explain to me how to get the answer and show your work, thank you)

1. Under the picture is a place to write each family member's name. Match the

name of the family members to each of the people in the family picture in

order from left to right.


2. Dana is five times as old as Alex. Write an expression to show the

relationship between Dana and Alex.


3. Two years ago, Elam was half as old as Dana. Write an equation to show

the relationship between Elam and Dana.


4. Elam is currently 31 years old. How old is Alex?

Show how you figured it out.

Answer 1

1. Label the people from left to right as:

Bo, Chris, Dana, Alex, Elam, Glyn, Frances

2. d = 5a

3. 2e = d + 2

4. Alex is 12.

Explanation:

1.

I am referring to every person starting from the left by position. When I write 1st, I mean the woman at the left of all people. 2nd is the girl holding hand with 1st. 3rd is the older man, etc.

It is hard to tell who the people are by age. Obviously, the adults are older than the children. The man third from left seems to be the oldest person. The youngest seems to be the 6th from the left. People of similar age are hard to put in age order, such as the children 4th and 7th from the left.

The sure way to put them in order is by height since the picture above shows clearly the order of their heights, and all heights are different.

In order of height according to the picture of the people, from tallest to shortest:

5th

3rd

1st

7th

4th

2nd

6th

Now we look in the graph. The heights are plotted along the horizontal axis, so the more to the right a name is, the taller a person is. Start from the right of the graph and read the names moving left. Ignore the position along the vertical axis of where the name is. In other words, ignore how high or low on the graph a name is. Just take into account how far right or left the name is.

Starting from the right and moving left, the names are (from tallest to shortest):

Elam

Dana

Bo

Frances

Alex

Chris

Glyn

Since we have two listings of the people by position and by name from tallest to shortest, we can now match the names to the heights.

Elam 5th

Dana 3rd

Bo 1st

Frances 7th

Alex 4th

Chris 2nd

Glyn 6th

Label the people from left to right as:

Bo, Chris, Dana, Alex, Elam, Glyn, Frances

2.

Let d = Dana's age

Let a = Alex's age

d = 5a

3.

Let e = Elam's age now.

Let d = Dana's age now.

Two years ago, Elam was e - 2, and Dana was d - 2.

e - 2 = (d - 2)/2

2e - 4 = d - 2

2e = d + 2

4.

e = 31

Use the answer to 3. to find the age of Dana.

2e = d + 2

2(31) = d + 2

62 = d + 2

d = 60

Dana is 60.

Now use the answer to 2. to find the age of Alex.

d = 5a

60 = 5a

5a = 60

a = 60/5

a = 12

Alex is 12.