I have a total of 325 in the coins of denominations 2, 5 and 10. The number of 2 coins is 5 times
the number of 5 coins. The total number of coins is 100. How many coins of each denomination are with me?
Answers
Step-by-step explanation:
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The total sum of money = 300
Let the number of 5 coins be x, number of 2 coins be 3x and number of 1 coin be 160-\left(x+3x\right)=160-4x160−(x+3x)=160−4x
According to question, 5\times x+2\times\left(3x\right)+1\times\left(160-4x\right)=3005×x+2×(3x)+1×(160−4x)=300
\Rightarrow\ 5x+6x+160-4x=300⇒ 5x+6x+160−4x=300
\Rightarrow\ 7x+160=300⇒ 7x+160=300
\Rightarrow7x+160-160=300-160⇒7x+160−160=300−160
[Subtracting 160 from both sides]
\Rightarrow\ 7x=140⇒ 7x=140
\Rightarrow\ \frac{7x}{7}=\frac{140}{7}⇒
7
7x
=
7
140
[Dividing both sides by 7]
x = 20
Hence, the number of coins of 5 denomination = 20
Number of coins of 2 denomination = 3 x 20 = 60
Number of coins of 1 denomination = 160 - 4 x 20 = 160 - 80 = 80
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