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A bag contains [tex]\(1p\)[/tex], [tex]\(2p\)[/tex], and [tex]\(5p\)[/tex] coins.

[tex]\(\frac{3}{8}\)[/tex] of the coins in the bag are [tex]\(1p\)[/tex] coins.

There are as many [tex]\(5p\)[/tex] coins as [tex]\(1p\)[/tex] coins in the bag.

There are 640 coins in total.

Work out the number of [tex]\(2p\)[/tex] coins in the bag.



Answer :

GinnyAnswer
Let's work through the problem step-by-step to find the number of 2 p coins in the bag.

1. Total number of coins:
There are a total of 640 coins in the bag.

2. Fraction of 1 p coins:
[tex]\(\frac{3}{8}\)[/tex] of the coins are 1 p coins.

3. Calculate the number of 1 p coins:
Given that [tex]\( \frac{3}{8} \)[/tex] of the total 640 coins are 1 p coins:
[tex]\[ \text{Number of 1 p coins} = \frac{3}{8} \times 640 = 240 \][/tex]

4. Number of 5 p coins:
It is given that the number of 5 p coins is the same as the number of 1 p coins:
[tex]\[ \text{Number of 5 p coins} = 240 \][/tex]

5. Calculate the remaining number of coins:
To find out how many 2 p coins there are, we subtract the number of 1 p and 5 p coins from the total number of coins:
[tex]\[ \text{Number of 2 p coins} = 640 - (\text{Number of 1 p coins} + \text{Number of 5 p coins}) \][/tex]
Substituting the values:
[tex]\[ \text{Number of 2 p coins} = 640 - (240 + 240) = 640 - 480 = 160 \][/tex]

Thus, the number of 2 p coins in the bag is:
[tex]\[ \boxed{160} \][/tex]

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