The gardener

The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?

Correct answer:

n =  16

Step-by-step explanation:

960 = cn (c−12)⋅ (n+4)=960  960 = cn cn + 4c − 12n − 48=960  960 + 4c − 12n − 48=960 4c − 12n=48 c − 3n=12 c = 12+3n  960 = cn  960=(12+3n)⋅ n  960=(12+3n)⋅ n −3n2−12n+960=0 3n2+12n−960=0 3 ...  prime number 12=22⋅3 960=26⋅3⋅5 GCD(3,12,960)=3  n2+4n−320=0  a=1;b=4;c=−320 D=b2−4ac=42−4⋅1⋅(−320)=1296 D>0  n1,2​=2a−b±D​​=2−4±1296​​ n1,2​=2−4±36​ n1,2​=−2±18 n1​=16 n2​=−20  n>0 n=n1​=16 c=12+3⋅ n=12+3⋅ 16=60

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