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[Maths]
A jeweller has bars of 18-carat gold and 11 carat gold. How much of each be melted together to obtain 16-carat gold weighing 120 grams? (Pure gold is 24-carat)
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Topic: Simultaneous Linear Equations
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Verified answer
Given and To Find:-
Let,
Then,
x + y = 120 —i
Substitute the values,
18x + 12y = 16*120
3x +2y =320 —ii
Subtracting ii from i,
3x+3y=360
3x+2y=320
y=40
Substituting the values,
x + y =120
x + 40=120
x = 120-40
x = 80
Therefore,
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[tex]\huge{\mathfrak\red{Solution♡}}[/tex]
Let us assume Xg and Yg be the weight of 18Karat 12Karat Gold respectively.
As per the condition given
[tex]\huge \frac{18x}{24} + \frac{12y}{24} = \frac{120 \times 16}{24} [/tex]
3x+2y= 320 --> Given condition i
x+y= 120 --> Given condition ii
x= 320-240= 80 in condition ii
180+y= 120--> y=40
Hence, the weight is 80g and 40g.
Khadijah21