Explanation
Multiplying equation (1) with 4 we get, 28x+24y=284 ----- equation (3)
Multiplying equation (2) with 3 we get, 15x−24y=−69 ----- equation (4)
Adding equations (4) and (3), we get 43x=215=>x=5
Substituting x=5 in the equation (2), we get
5(5)−8y=−23=>y=6
Substituting y=14 in the equation (1), we get
x+14=2(x)(14)
∴
Multiplying eq(1) with 3 we get,
\dfrac {60}{x+y} + \dfrac {9}{x-y} = 21 ...(3)
Multiplying eq(2) with 4 we get,
\dfrac {32}{x-y} - \dfrac {60}{x+y} = 20 ...(4)
Adding eq(3) and eq(4), we get
\dfrac {41}{x-y} = 41 => x - y = 41 ...(5)
Substituting x-y = 41 in the eq(1), we get
\dfrac {20}{x+y} + \dfrac {3}{1} = 7 => \dfrac {20}{x+y} = 4 => x +y = 5 ... (6)
Adding eq(5) and eq(6), we get
2x = 6 => x = 3
Substituting x = 3 in the eq(5), we get
3-y = 1 => y = 2
As per the statement, "If A gives 10 pencils to B, then B will have twice as many as A":
\implies 2(x - 10) = y + 10
2x - y = 30 --- (1)Also, as per the statement, "if B gives 10 pencils to A, then they will have the same number of pencils"
\implies x + 10 = y - 10
x - y = -20 --- (2)
Subtracting equation (2) from (1) , we get:
2x-y-x+y=30+20
x = 50
Substituting x = 50 in equation (2) , we get:
50 -y = -20
\implies y = 70
So, A has 50 pencils and B has 70 pencils.
Multiplying equation (1) with 5 We get 5x + 5y = 35 ...(3)Adding equations (2) and (3), 4x-5y=-8 5x+5y=35 ______________ 9x\ \ \ \ \ \ \ \ =27
\Rightarrow 9x = 27 \Rightarrow x = 3 Substituting x = 3 in the equation (1) We get 3 + y = 7 \Rightarrow y = 4
Hence, the fraction is \dfrac34
Multiplying equation (1) with 3 we get, 3x + 3y = 552 ----- equation (3)
Adding equations 2 and 3 , we get 10x = 636 => x = 63.6
Substituting x = 63.6 in the equation (2) , we get 63.6 + y = 184 =>y = 120.4
Thus , the parts are 63.6 ; 120.4
Multiplying equation (2) with 1.05 we get, 1.1235x + 1.1025y = 1223.25 ----- equation (4)
Subtracting equation (4) from (3) , we get 0.0424y = 25.44 \Rightarrow y = 600
Substituting y = 600 in the equation (2) , we get 1.07x + 1.05(600) = 1165 \Rightarrow x = 500 Hence, cost price of A is Rs. 500 and of B is Rs. 600
Substituting y = 18 in the equation (1) , we get x + 18 = 40 => x = 22
Hence 22 kg and 18 kg of two types of sweets were bought.
Substituting x = 600 in the equation (1) , we get 600 + y = 1250 \Rightarrow y = 650
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