Question 696847

1. Mike is 20 cm shorter than Tim
2. Jane is 25 cm taller than Tim
3. Jill is 21 cm shorter than Jack
4. Tom is 38 cm taller than Mike
5. Jake is 36 cm shorter than Mark
6. Mark is 8 cm taller than Jane
7. Jill is 11 cm shorter than Jake
8. Tom is 183 cm tall

How tall is Jack?


Let Tim’s height be T
Then Mike’s is: T – 20 cm


Let Jack’s be J
Then Jill’s is: J - 21 cm


Jane’s is: T + 25 cm
Tom’s is: T – 20 + 38, or T + 18 cm


Let Mark’s height be M
Then Jake’s is: M – 36 cm
Also, M = T + 25 + 8, or M = T + 33 cm
J – 21 = M – 36 – 11, or M = J – 21 + 47, or M = J + 26 cm


Since Tom is 183 cm tall, then T + 18 = 183 ---- T, or Tim is 183 – 18, or 165 cm
Since M = T + 33, and M = J + 26, then: T + 33 = J + 26
165 + 33 = J + 26 ------ Substituting 165 for T 
J, or Jack’s height = 198 – 26, or {{{highlight_green(172)}}} cm 


You can do the check!!


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