Bicycles

You're the owner of the transport 's learning playground. Buy bicycles of two colors but you've got to spend accurately 120000 Kč. Blue bike costs 3600Kč and red bicycle 3200Kč.

Result

a₁ =  4
b₁ =  33
a₂ =  12
b₂ =  24
a₃ =  20
b₃ =  15
a₄ =  28
b₄ =  6

Solution:

$120000=3600a + 3200b \ \\ n=0,1,2,3 \ \\ n=0 \ \\ a_{1}=8 \cdot \ n+4=8 \cdot \ 0+4=4$

$b_{1}=33-9 \cdot \ n=33-9 \cdot \ 0=33$

$n=1 \ \\ a_{2}=8 \cdot \ n+4=8 \cdot \ 1+4=12$

$b_{2}=33-9 \cdot \ n=33-9 \cdot \ 1=24$

$n=2 \ \\ a_{3}=8 \cdot \ n+4=8 \cdot \ 2+4=20$

$b_{3}=33-9 \cdot \ n=33-9 \cdot \ 2=15$

$n=3 \ \\ a_{4}=8 \cdot \ n+4=8 \cdot \ 3+4=28$

$b_{4}=33-9 \cdot \ n=33-9 \cdot \ 3=6$

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