Question

daca se impart cate 16 , cate 8 sau cate 20 merele dintr-un magazin ,raman de fiecare dat 10 mere .stiind ca in magazin sunt mai mult de 1000de mere aflati numarul minim de mere

Answer 1

fie m  numarul de mere din magazin
m=16a+10
m=8b+10
m=20c+10


m-10=16a
m-10=8b
m-10=20c

8 | m-10
16| m-10
20 |m-10

cmmmc(8,16,20) |m-10

8=2³
16=2^4
20=2² * 5
cmmmc (8.16,20)=2^4 *5=16*5=80
ceilalti multimpli comuni vor fioi din M80

m-10 =80k
m=80k+10
 80k+10>1000, 80k+10 minim
80k>990, 80k minim
 8k>99, 8k miinim
k>99/8. k∈N, k minim
k>12,3..k∈N, k minim
k=13

m=80k+10=80*13+10=1050 mere, cerinta