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 (c12) (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 3n212n+960=0 3n2+12n960=0 3 ...  prime number 12=223 960=2635 GCD(3,12,960)=3  n2+4n320=0  a=1;b=4;c=320 D=b24ac=4241(320)=1296 D>0  n1,2=2ab±D=24±1296 n1,2=24±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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