Ornamental shrubs

Children committed to plant 240 ornamental shrubs. Their commitment however exceeded by 48 shrubs. Write ratio of actually planted shrubs and commitment by lowest possible integers a/b.

Correct result:

a =  6
b =  5

Solution:

$$\begin{gathered} x=240 \\ y=x+48=240+48=288 \\ 288=2^5\cdot 3^2 \\ 240=2^4\cdot 3\cdot 5 \\ \text{GCD}(288,240)=2^4\cdot 3=48 \\ d=GCD(y,x)=GCD(288,240)=48 \\ a=y\mathrm{/}d=288\mathrm{/}48=6 \end{gathered}$$

$b=x\mathrm{/}d=240\mathrm{/}48=5$

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