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Question

Sam is 5 times as old as his sister. In 10 years time, Sam will be 12 years less than thrice his sister’s age then. How much older is Sam than his sister?

Source: Nan Chiau Primary

Answer

Now

Sam                          X  X  X  X  X  [5u]

Sister                        X                     [u]

10 yrs later

Sam                10 +   X  X  X  X  X—-> (1) [10+5u] This sum is 12 yrs less than (2)

Sister              10 +   X

(3x Sister)     30 +  X  X X ——–> (2) [30+3u]

By cancelling out “X X X” in the model:

Comparing (1) and (2): 10 + X +X + 12 = 30 –> X=4

By equations:

Comparing (1) and (2): [10 + 5u] + 12 = [30+3u] –> u=4

Sam is 16 years older than his sister now (difference of 4u = 16)#


Checking:

                  Now                 +10 yrs later

Sam            20                  30

Sister           4                   14

3x Sister                           42 (12 more than Sam) 

0 Replies 2 Likes ✔Accepted Answer

16 years older

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Sam is 5 times as old as his sister. In 10 years time, Sam will be 12 years less than thrice his sister’s age then. How much older is Sam than his sister?

5unit + 10 = 3 (unit+10) – 12   

Sister = 4 year old

Sam = 20 years old

Ans = 16 years

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This a Before After question.

 

   SAM

Sister 

Total      
 Before  5u  1u        
 After  5u + 10  1u + 10        
    3u + 30        

 

5u + 10 + 12 = 3u + 30

5u – 3u = 30 – 22

2u = 8

1u = 4

4u = 4 × 4 = 16 ##

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post-19301
0 Replies 1 Like