Question

$\textbf{any maths aryabhatta help me in this plzz.} \:$
the cost of 8 apples and 5 mangoes is rs194. the cost of 5 guvavas and 6 mangoes is rs183. the cost of 7 apples and 9 guvavas is rs226.

what is the cost of 3 mangoes, 2 guvavas and 1 apple together ?

$\textsf{no spam and wrong answer.}$
​

Answer 1

Solution :-

8A + 5M = 194 ------- Equation ❶

5G + 6M = 183 ------- Equation ❷

7A + 9G = 226 ------- Equation ❸

Now 6*(Equation ❶) - 5(Equation ❷) , we get :-

➺ 6(8A + 5M) - 5(5G + 6M) = 6*194 - 5*183

➺ 48A + 30M - 25G - 30M = 1164 - 915

➺ 48A - 25G = 249 -------- Equation ❹

________________________

Now, Equation ❸ + (9/25)[Equation ❹] we get,

➻ (7A + 9G) + [(9/25)(48A - 25G)] = 226 + [(9/25) * 249]

➻ [7A + (48*9A/25)] = (249*9/25) + 226

⟪ Now, Here we have use a Little approximation for making calculation easy (48/25) = 2 & (249/25) = 10. ⟫

So,

➻ (7A + 2*9A) = 10*9 + 226

➻ 25A = 316

➻ A ≈ 13 .

______________________

Putting value of A in Equation ❶ :-

⟼ 8*13 + 5M = 194

⟼ 5M = 194 - 104

⟼ 5M = 90

⟼ M = 18

________________

Putting value of M in Equation ❷ Now :-

⟿ 5G + 6*18 = 183

⟿ 5G = 183 - 108

⟿ 5G = 75

⟿ G = 15

___________________

Hence, we have :-

☞ A = 13

☞ M = 18

☞ G = 15

Therefore,

☛ Cost of (3M + 2G + A)

☛ (3*18 + 2*15 + 13)

☛ (54 + 30 + 13)

☛ Rs.97 (Ans.)

Answer 2

$\tt{\huge{\orange { --------------- }}}$

QUESTION :

$\textbf{any maths aryabhatta help me in this plzz.} \:$

the cost of 8 apples and 5 mangoes is rs194. the cost of 5 guvavas and 6 mangoes is rs183. the cost of 7 apples and 9 guvavas is rs226.

what is the cost of 3 mangoes, 2 guvavas and 1 apple together ?

$\textsf{no spam and wrong answer.}$

CONCEPT USED :

Solving a system of Linear equations.

SOLUTION :

From the above Question, we can derive the following equations.

First let us assume the following...

Let the cost of 1 Apple be Rs. A

Let the cost of 1 Mangoe be Rs. M

Let the cost of 1 Guava be Rs. G

So, we can form :

8 A + 5 M = 194....... ( 1 )

5 G + 6 M = 183. ........... ( 2 )

7 A + 9 G = 226. ... ..... ( 3 )

TO FIND :

3M + 2 G + 1 A = ?

CALCULATION :

From equation 1, we can form :

5 m = - 8 A + 194

=> m = { - 8 / 5 } A + { 194 / 5 }........ ( 5 )

Substituting this in Equation 2..

=> 5 G + 6 { { - 8 / 5 } A + { 194 / 5 } } = 183

=> 5 G + { -48 / 5 } A + { 194 / 5 } = 183

=> 5 G = { 48 / 5 } A + 183 - { 194 / 5 }

=> 5 G = { 48 / 5 } A - { 721 / 5 }

=> G = { 48 / 25 } A - { 721 / 25 }......... ( 6 )

Substituting this in Equation 3..

=> 7 A + 9 G = 226

=> 7 A + 9 { { 48 / 25 } A - { 721 / 25 } } = 226

Solving for A, we get :

A = 13

Substituting for G , we get :

G = { 48 / 25 } × 13 - { 721 / 25 }

=> G = 15

Substituting for M , we get :

=> M = { - 8 / 5 } A + { 194 / 5 }

Solving,

M = 18.

Cost of 3 mangoes = 3 × 18 = Rs. 54

Cost of 2 Guavas = 2 × 15 = Rs. 30

Cost of 1 Apple = Rs. 13

Hence, the total cost comes out to be Rs. 97

ANSWER :

Therefore the cost of 3 mangoes, 2 guvavas and 1 apple together is Rs. 97.