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)
∴x=−12
Multiplying eq(1) with 3 we get,
60x+y+9x−y=21 ...(3)
Multiplying eq(2) with 4 we get,
32x−y−60x+y=20 ...(4)
Adding eq(3) and eq(4), we get
41x−y=41=>x−y=41 ...(5)
Substituting x−y=41 in the eq(1), we get
20x+y+31=7=>20x+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":
⟹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"
⟹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
⟹y=70
So, A has 50 pencils and B has 70 pencils.
Multiplying equation (1) with 5We get 5x+5y=35 ...(3)Adding equations (2) and (3), 4x−5y=−8 5x+5y=35 ______________ 9x =27
⇒9x=27⇒x=3Substituting x=3 in the equation (1) We get 3+y=7⇒y=4
Hence, the fraction is 34
Multiplying equation (1) with 3 we get, 3x+3y=552 ----- equation (3)
Adding equations 2 and 3, we get 10x=636=>x=63.6
Substitutingx=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⇒y=600
Substituting y=600 in the equation (2), we get 1.07x+1.05(600)=1165⇒x=500Hence, 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 22kg and 18kg of two types of sweets were bought.
Substituting x=600 in the equation (1), we get 600+y=1250⇒y=650
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