In a collection of rare coins, there is one gold coin for every four non-gold coins. If 20 more gold coins are added to the collection, the ratio of the number of gold coins to that of non-gold coins will be 2:3. The total number of coins in the collection will now become ________.

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Let the number of gold coins be G and the number of non-gold coins be N.

Given the initial ratio:
G : N = 1 : 4
So, G = x and N = 4x for some x.

After adding 20 gold coins, the new number of gold coins = G + 20 = x + 20.
The number of non-gold coins remains the same = 4x.

The new ratio is given as:
(G + 20) : N = 2 : 3
=> (x + 20) / 4x = 2 / 3
Cross multiply:
3(x + 20) = 8x
3x + 60 = 8x
60 = 8x - 3x
60 = 5x
x = 12

Now, initial gold coins G = x = 12
Initial non-gold coins N = 4x = 48

After adding 20 gold coins, total gold coins = 12 + 20 = 32
Total coins = gold + non-gold = 32 + 48 = 80

Hence, the total number of coins in the collection now is 80.

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