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Svetach [21]
2 years ago
8

victor are 60 de lei si merge la florarie pentru a-i cumpara mamei sale un buchet de flori. daca ar cumpara 9 garoafe si 4 trand

afiri, ar plati 47 de lei. daca ar cumpara doar trandafiri, toti banii i-ar ajunge pentru 12 bucati. insa el cumpara 13 flori (garoafe si trandafiri) si ramane cu 5 lei rest, cate garoafe si cati trandafiri a cumparat victor?
Mathematics
1 answer:
Alja [10]2 years ago
4 0

Answer:

Număr de trandafiri = x = 5 trandafiri

Numărul este garoafe = y = 8 garoafe

Step-by-step explanation:

Pasul 1

Să reprezentăm:

Costul garoafelor = c

Costul trandafirilor = r

Victor are 60 de lei și merge la florărie să-i cumpere mamei sale un buchet de flori.

Dacă ar cumpăra 9 garoafe și 4 trandafiri, ar plăti 47 de lei.

Prin urmare,

9c + 4r = 47 ..... Ecuația 1

Dacă ar cumpăra doar trandafiri, toți banii ar fi suficienți pentru 12 bucăți.

Prin urmare,

12 trandafiri = 60 lei

1 trandafir = r lei

Cross Multiply

12r = 60 lei

r = 60 lei / 12

r = 5 lei

1 trandafir costă 5 lei

Înlocuim 5 cu r în ecuația 1

9c + 4 × 5 = 47

9c + 20 = 47

Colectează ca termeni

9c = 47 - 20

9c = 27

c = 27/9

c = 3 lei

Costul unei garoafe este de 3 lei

Pasul 2

Dar cumpără 13 flori (garoafe și trandafiri) și rămâne cu 5 lei rămași,

60 lei - 5 lei = 55 lei

Asta înseamnă că a cheltuit 55 de lei pe 13 flori.

Lasă

Număr de trandafiri = x

Numărul este garoafe = y

x + y = 13 ......... Ecuația 1

x = 13 - y

Din moment ce, Costul unei garoafe = 3 lei și 1 trandafir = 5 lei

3x + 5y = 55 ...... Ecuația 2

Înlocuim 13 - y cu x în ecuația 2

3x + 5y = 55

3 (13 - y) + 5y = 55

39 - 3y + 5y = 55

Colectează ca termeni

- 3y + 5y = 55 - 39

2y = 16

y = 16/2

y = 8

Rezolvarea pentru x

x = 13 - y

x = 13 - 8

x = 5

Prin urmare:

Număr de trandafiri = x = 5 trandafiri

Numărul este garoafe = y = 8 garoafe

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