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 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

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

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

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

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

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

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

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)+1+1 + x+1 = 22

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)+1+1 + x+1 = 22 2x - 2 +1 +1 + x+1 = 22 3x +1 = 22 3x = 21 x = 7

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)+1+1 + x+1 = 22 2x - 2 +1 +1 + x+1 = 22 3x +1 = 22 3x = 21 x = 7 check

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)+1+1 + x+1 = 22 2x - 2 +1 +1 + x+1 = 22 3x +1 = 22 3x = 21 x = 7 check

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)+1+1 + x+1 = 22 2x - 2 +1 +1 + x+1 = 22 3x +1 = 22 3x = 21 x = 7 check

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.

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

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 22 - (x+1) John’s age x x+1

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

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 7 = x