Question

Help please :)

I have a total of rupees 300 coins in denomination rupee 1, rupee 2 and rupee 5.The total number of 2 rupee coins is three times the number of rupee 5 coins.The total number of coins is 160.How many coins of each denomination are with me?

Class 8 CBSE
Linear equations in one variable
Exercise 3.2
16th question..​

Answer 1

Let the number of coin 5 = Rs.x

so the number of coin 2 = 3x

so the number of coin 1 = 160 - 4x

so amount of rs.5 = 5x

so the amount of rs.2 = 6x

a/q

5x + 6x + 160 - 4x = 300

7x = 300 - 160

7x = 140

x = 20

so the number of coin of Rs.5 = 20 coins

so the number of coin of Rs.2 = 60 coins

so the number of coin of Rs.1 = 80 coins

Answer 2

Given :-

Total amount = Rs. 300

Rupees 300 in denominators of Rs. 1, Rs. 2 and Rs. 5

Number of Rs 2 coins = 3 times number of Rs 5 coins

Total number of coins = 160

To Find :-

Number of ₹5 coins.

Number of ₹2 coins.

Number of ₹1 coins.

Solution :-

Given that,

Total amount = Rs. 300

Rs. 300 of denomination rupee 1, rupee 2 and rupee 5.

According to the question,

Let the number of ₹5 coins be x

Then,

Number ₹2 coins = 3x

Number of ₹1 coins = $\sf (160-4x)$

Value of ₹5 coins = $\sf x \times 5 = 5x$

Value of ₹2 coins = $\sf 3x \times 2 = 6x$

According to the given info,

$\sf 5x + 6x + (160 - 4x) = 300$

$\implies \sf 11x + 160 - 4x = 300$

$\implies \sf 7x = 140$

$\implies \sf x=\dfrac{140}{7}$

$\implies \sf x = 20$

Now, substituting the values,

Number of ₹5 coins = $\sf x=20$

Number of ₹2 coins = $\sf 3x=3 \times 20=60$

Number of ₹1 coins = $\sf (160 - 4x) = 160 - 80 = 80$