Equations for ages

Equations for ages

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This task is about using equations to find out people's ages.
Prisha and Nikau were writing equations for the ages of people in their families.
Write an equation for each problem and use it to find the person's age.
Simone      Nick
a)
Prisha said that if you doubled her sister's age and added 5 the result would be 25.
 
i)   Complete this equation to find her sisters's age (s). ____________________ = 25
 
ii)   How old is Prisha's sister? ____________________
 
b)
Nikau said that his sister is 4 times as old as his brother, and together their ages add to 20.
 
i)   Complete this equation to find his brother's age (b). ____________________ = 20
 
ii)   How old is Nikau's brother? ____________________
 
c)
If you multiplied Prisha's father's age by 4 and subtracted 84, the answer is the same as if you doubled her father's age.
 
i)    Write an equation to find her father's age (f). ____________________
 
ii)   How old is Prisha's father? ____________________
 
d)
Nikau's mother was 30 when he was born. She is now 3 times as old as Nick.
 
i)    Write an equation to find Nikau's age (n). ____________________
 
ii)   How old is Nikau's mother? ____________________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Description of task: 
Students write and solve equations for story problems describing practical situations.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y10 (11/1999)

a)

i)
ii)

2s + 5
10

moderate
very easy

b)

i)

ii)

4b + b or 5
[Accept equivalent equations]
4

difficult

moderate

c)

i)

ii)

4f - 84 = 2f  
[Accept equivalent equations]
42

difficult

difficult

d)

i)

ii)

3n - n = 30 or 3n = 30 + n  
[Accept equivalent equations]
45

very difficult

difficult

NOTE: Accept terms like 2 × s as being equivalent to 2s.

Diagnostic and formative information: 

 

Common error

Likely calculation

Likely reason

a) i)

    ii)

10 + 10 + 5
2 × 10 + 5
4 × 4 + 4

 

Shows numerical calculation rather than an equation with a variable.

b) i)
    ii)

4b = 20
5

20 ÷ 4

Takes sister's age as 20 rather than combined ages = 20.