# 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

5 Answers

# 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)

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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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