Question

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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​

Answer 1

Given and To Find:-

• 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)

Let,

• Quantity of 18 carat gold be x
• Quantity of 12 carat gold be y

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,

• Quantity of 18 Carat gold = 80gm
• Quantity of 16 Carat gold = 40gm

★ Hope it helps u ★

Answer 2

$\huge{\mathfrak\red{Solution♡}}$

Let us assume Xg and Yg be the weight of 18Karat 12Karat Gold respectively.

As per the condition given

$\huge \frac{18x}{24} + \frac{12y}{24} = \frac{120 \times 16}{24}$

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