Sure, let's solve the problem step by step.
First, let's understand the given data:
- The total number of coins in the bag is 640.
- [tex]\(\frac{3}{8}\)[/tex] of the coins are 1 p coins.
- The number of 5 p coins is the same as the number of 1 p coins.
Let's denote the total number of 1 p coins as [tex]\( x \)[/tex].
Step 1: Calculate the number of 1 p coins.
Given that [tex]\(\frac{3}{8}\)[/tex] of the total coins are 1 p coins:
[tex]\[ x = \frac{3}{8} \times 640 \][/tex]
[tex]\[ x = 240 \][/tex]
So, there are 240 coins of 1 p.
Step 2: Calculate the 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. Therefore, the number of 5 p coins is also:
[tex]\[ 240 \][/tex]
Step 3: Calculate the total number of 1 p and 5 p coins together.
The total number of 1 p and 5 p coins is:
[tex]\[ 240 + 240 = 480 \][/tex]
Step 4: Calculate the number of 2 p coins.
The remaining coins in the bag are all 2 p coins. Therefore, the number of 2 p coins is the total number of coins minus the total number of 1 p and 5 p coins:
[tex]\[ 640 - 480 = 160 \][/tex]
Therefore, there are [tex]\( 160 \)[/tex] coins of 2 p in the bag.
