In January of 2005, Donatello was one more than eleven times as old as Leonardo. In January of 2014, Donatello was seven more than three times as old as Leonardo. Which of the following statements are true? Check all that apply.

In January of 2005, Leonardo was 3.

In January of 2005, Donatello was 23.

In January of 2014, Leonardo was 15.

In January of 2014, Donatello was 43.

Leonardo is older than Donatello.

Donatello is older than Leonardo.

Let's just make up some variables.

D = Donatello's age in 2005, L = Leo's

(D + 9) = Donatello's age in 2014.

D = 11L + 1

(D + 9) = 3 (L + 9) + 7

We need to get one variable on its own in both equations to use substitution:

D = 11L + 1

D + 9 = 3 (L + 9) + 7

D + 9 = 3L + 27 + 7

D = 3L + 27 + 7 - 9

D = 3L + 25

Now we can substitute 3L + 25 for D in the other equation to solve for L.

D = 11L + 1

3L + 25 = 11L + 1

24 = 8L

L = 3

Use L = 3 in an earlier equation to find D.

D = 11L + 1

D = 11*3 + 1

D = 33 + 1

D = 34

Now we know that in 2005, Leo was 3 and Don was 34.

In 2005, Leo was 3 - - true

In 2005, Don was 23 - - fasle

In 2014, Leo was 15 - - fasle (3+9=12)

In 2014, Don was 43 - - true (34+9=43)

Leo is older than Don - - false

Don is older than Leo - - true