Wagons and cranes

The same cranes are unloading 96 wagons.
There would be fewer wagons for each crane if there were two more cranes.
How many cranes were there?

Final Answer:

n =  4

Step-by-step explanation:

nv = 96 (n+2)(v−8) = 96 nv +2v −8n − 16 = 96 96 +2⋅ 96/n−8n − 16 = 96 2⋅ 96−8n2−16n=0  2⋅ 96−8n2−16n=0 −8n2−16n+192=0 8n2+16n−192=0 8=23 16=24 192=26⋅3 GCD(8,16,192)=23=8  n2+2n−24=0  a=1;b=2;c=−24 D=b2−4ac=22−4⋅1⋅(−24)=100 D>0  n1,2​=2a−b±D​​=2−2±100​​ n1,2​=2−2±10​ n1,2​=−1±5 n1​=4 n2​=−6 n>0 n=n1​=4 v1​=96/n=96/4=24 v2​=96/(n+2)=96/(4+2)=16 n=4

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