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.

Result

a =  6
b =  5

Solution:

x=240 y=x+48=240+48=288 288=2532 240=2435 GCD(288,240)=243=48  d=GCD(y,x)=GCD(288,240)=48 a=y/d=288/48=6x=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/d=288/48=6
b=x/d=240/48=5b=x/d=240/48=5



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