An alchemist discovered that the formula to turn ordinary me

Question

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

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

mansoorfarooqui · Answer

best approach would be to plug in answer choices.

start with C:
M=22.5
2M=45
G = 22.5*3/2+15 as it would have a fractional part.. skip it
choose a number which wont result in fractional part so A and D remains

Take D:
M=30
2M=60 which should be our target value

put M=30 we get G=60
so D is the answer

shanmugamgsn · Answer

Hey Mansoor,
"a metal bar weighs twice as much as a gold bar"
this doesnt mean
M=2G ?

Marcab · Answer

A time saving method:
Since we know that  Integer+Integer=Integer , and number of bars can't be in fractional form, therefore  3M/2  must be an integer or M must be a multiple of 2.
The only options that we have is A and D.
On putting 10 and 30 respectively, we find that 30 fits the conditions.
Hence 30 is the answer.

Rock750 · Answer

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

ziko · Answer

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?

Rock750 · Answer

Did u get D using M=2G ?

ziko · Answer

No i did not, that s why i raised this question, to clarify where i did wrong? or where exactly i am loosing the track.

KarishmaB · Answer

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)

Naif945 · Answer

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.

Bunuel · Answer

Maybe this will help.

Since  G = \frac{3}{2}M + 15 , then  M = 30  metal bars will give  G = \frac{3}{2}M + 15 = 60  gold bars, and since a metal bar weighs twice as much as a gold bar, the wight of   M = 30  metal bars will the same as the weight of   G = 60  gold bars.

An alchemist discovered that the formula to turn ordinary me

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