1. Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______

2. last year now next year Mary’s age John’s age
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
John’s age

3. last year now next year Mary’s age John’s age x
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
John’s age x

4. last year now next year Mary’s age John’s age x - 1 x
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
John’s age
x - 1 x

5. last year now next year Mary’s age John’s age x - 1 x
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
John’s age
x - 1 x

6. last year now next year Mary’s age 2(x – 1) John’s age x - 1 x
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
2(x – 1)
John’s age
x - 1 x

7. last year now next year Mary’s age 2(x – 1) John’s age x - 1 x
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
2(x – 1)
John’s age
x - 1 x

8. last year now next year Mary’s age 2(x – 1) 2(x – 1) +1 2(x – 1)+1+1
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
2(x – 1)
2(x – 1) +1
2(x – 1)+1+1
John’s age
x - 1 x
x + 1

9. last year now next year Mary’s age 2(x – 1) 2(x – 1) +1 2(x – 1)+1+1
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
2(x – 1)
2(x – 1) +1
2(x – 1)+1+1
John’s age
x - 1 x
x + 1
Mary’s age next year John’s age next year = 22
2(x-1) x = 22

10. last year now next year Mary’s age 2(x – 1) 2(x – 1) +1 2(x – 1)+1+1
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
2(x – 1)
2(x – 1) +1
2(x – 1)+1+1
John’s age
x - 1 x
x + 1
Mary’s age next year John’s age next year = 22
2(x-1) x = 22
2x x = 22
3x = 22
3x = 21
x = 7

11. last year now next year Mary’s age John’s age 7
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
John’s age 7
Mary’s age next year John’s age next year = 22
2(x-1) x = 22
2x x = 22
3x = 22
3x = 21
x = 7
check

12. last year now next year Mary’s age 12 John’s age 6 7
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age 12
John’s age 6 7
Mary’s age next year John’s age next year = 22
2(x-1) x = 22
2x x = 22
3x = 22
3x = 21
x = 7
check

13. last year now next year Mary’s age 12 13 14 John’s age 6 7 8
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age 12 13 14
John’s age 6 7 8
Mary’s age next year John’s age next year = 22
2(x-1) x = 22
2x x = 22
3x = 22
3x = 21
x = 7
check

14. Use some of the given information to name the numbers and
the rest to write the equation.
Here is another way to do the same problem.

15. last year now next year Mary’s age John’s age x x+1
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
John’s age x
x+1

16. last year now next year Mary’s age 22 - (x+1) John’s age x x+1
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
(x+1)
John’s age x
x+1

17. last year now next year Mary’s age 22-(x+1)-1-1 22-(x+1)-1 22 -(x+1)
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
22-(x+1)-1-1
22-(x+1)-1
22 -(x+1)
John’s age
x-1 x
x+1

18. last year now next year Mary’s age 22-(x+1)-1-1 22-(x+1)-1 22 -(x+1)
Last year Mary was twice as old as John.
Next year the sum of their ages will be 22.
How old is John now?_______
last year
now
next year
Mary’s age
22-(x+1)-1-1
22-(x+1)-1
22 -(x+1)
John’s age
x-1 x
x+1
Mary’s age last year = 2( John’s age last year )
20 – ( x+1 ) = 2( x-1)
19 – x = 2x - 2
= 3x
= x