An alchemist discovered that the formula to turn ordinary me

An alchemist discovered that the formula to turn ordinary metal into gold is \(G = \frac{3}{2}M + 15\), where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?

A. 10
B. 15
C. 22.5
D. 30
E. 67.5

Since a metal bar weighs twice as much as a gold bar, 2M = G

Thus, by the equation given :
2M = (3/2 *M) + 15
M/2 = 15

M = 30

Hence,

Answer : D

Well here i faced confusion, i thought if 1 bar of mettal is twice havier than 1 bar of gold, for example 1 bar of M=4 kg then 1 bar of G=2 kg, that means 4=2*2 --> M=2G but not 2M=G, So according to my initial calculation i stuck then i decided to plug in and found D plausable.

But could anyone suggest whether my initial thinking was wrong?

Did u get D using M=2G ?

Well here i faced confusion, i thought if 1 bar of mettal is twice havier than 1 bar of gold, for example 1 bar of M=4 kg then 1 bar of G=2 kg, that means 4=2*2 --> M=2G but not 2M=G, So according to my initial calculation i stuck then i decided to plug in and found D plausable.

But could anyone suggest whether my initial thinking was wrong?

Notice that M is the number of metal bars (not their weight)
And G is the number of gold bars.

If weight of a metal bar is twice the weight of a gold bar, and if you want to equate their weights, you will need twice the number of gold bars to make their weights equal.

That is how you get 2M = G (Number of gold bars should be twice the number of metal bars)

An alchemist discovered that the formula to turn ordinary metal into gold is \(G = \frac{3}{2}M + 15\), where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?

A. 10
B. 15
C. 22.5
D. 30
E. 67.5­


­Question statement is "Metal bar weighs twice as much as gold bars"
this means;
m=2g                (where m is metal bar weight & g is gold bar weight)

Now we need to get an equation having a variable of "No. of bars, not weight"
Suppose 
M= No. of metal bar
G= No. of gold bar

above equation tells;
If the metal bar weight 4kg then the gold bar weight would be 2kg. Now consider this in terms of no. of bars, to equate 1bar of metal we need 2 bars of gold.

So, the equation would be
M=2G

2M = G didn't make any kind of understanding.