Question

Boiz 10 si 11!
Va rog frumos! VA dau coroana si krabby patty

Answer 1

Problema 10:

Notații:

kg portocale = p

kg banane = b

$\left \{ {{7b\ +\ 2p\ =\ 66}\ |\ {\cdot}\ (-3) \atop {5b\ +\ 3p\ =\ 55}\ |\ {\cdot}\ 2 \right.{\iff}\left \{ {{-21b\ -\ 6p\ =\ -198} \atop {10b\ +\ 6p\ =\ 110}} \right.\\\\\implies -11b\ =\ -88\\\implies\ \ \ \ \ \ b\ =\ 8\\\\5b\ +\ 3p\ =\ 55\\40\ +\ 3p\ =\ 55\\3p\ =\ 55\ -\ 40\\3p\ =\ 15\\\implies p\ =\ 5$

R: 1 kg de banane costă 8 lei, iar 1 kg de portocale costă 5 lei.

Problema 11:

Notații:

primul număr - a

al doilea număr - b

$\left \{ {{a-b\ =\ 335} \atop {a\ :\ b\ =\ 12\ r\ 5}} \right. {\iff}\left \{ {{a\ -\ b\ =\ 335} \atop {a\ =\ 12b\ +\ 5}} \right. {\iff}\left \{ {{12b+5 -b\ =\ 335} \atop {a\ =\ 12b\ +\ 5}} \right.{\iff}\left \{ {{11b\ =\ 330} \atop {a\ =\ 12b+5}} \right.  {\iff}\left \{ {{b\ =\ 30} \atop {a\ =\ 365} \right.$

Proba:

$a-b=335\\365-30=335\ (A)\\\\a:b=12\ r\ 5\\365:30=12\ r\ 5\\{[365=(30{\cdot}12)+5]}\ (A)$

Answer 2

10

$b = banane$

$p = portocale$

$7 \: kg \: b + 2 \: kg \: p = 66 \: lei \: ( \times 3)$

$5 \: kg \: b + 3 \: kg \: p = 55 \: lei \: ( \times 2)$

$21 \: kg \: b + 6 \: kg \: p = 198$

$10 \: kg \: b + 6 \: kg \: p = 110$

$11 \: kg \: b = 88$

$b = 8$

$7 \times 8 + 2 \: kg \: p = 66 \: lei$

$2 \: kg \: p = 66 - 56$

$2 \: kg \: p = 10$

$p = 5$

11

$a - b = 335$

$a \div b = 12r5$

$a = 12b + 5$

$12 + 5 - b = 335$

$11b = 335 - 5$

$11b = 330$

$b = \frac{330}{11}$

$b = 30$

$a - 30 = 335$

$a = 335 + 30$

$a = 365$

$verificare = 365 - 30 = 335 \: (corect)$