Question

I have a total of rupees 300 in coins of denomination rupees 1 rupees to and rupees 5 the number of rupees to coins is three times the number of rupees 5 coins the total number of coins is 160 how many coins of each denomination are with me

Answer 1

Answer:

Given, total value of Rs = Rs 300

Total number of coins = 160

Coins of denomination = Re 1, Rs 2 and Rs 5

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

Let the number of coins of Rs 5 = m

Since, the number coins of Rs 2 is 3 times of the number of coins of Rs 5

Therefore, number of coins of Rs 2 = m x 3 = 3m

Now, Number of coins of Re 1 = Total number of coins – (Number of Rs 5 coins + Number of Rs 2 coins)

Therefore,

Number of coins of Re 1 = 160 – (m + 3m) = 160 – 4m

Total Rs = (Re 1 x Number of Re 1 coins) + (Rs 2 x Number of Rs 2 coins) + (Rs 5 x Number of Rs 5 coins)

⇒ 300 = [1 x (160 – 4m)] + (2 x 3m) + (5 x m)

⇒ 300 = (160 – 4m) + 6m + 5m

⇒ 300 = 160 – 4m + 6m + 5m

⇒ 300 = 160 – 4m + 11m

⇒ 300 = 160 + 7m

After transposing 160 to LHS, we get

300 – 160 = 7m

⇒ 140 = 7 m

After dividing both sides by 7, we get

Solution of exercise 2.2 Linear equations in one variable class eight math25

Thus, number of coins of Rs 5 = 20

Now, since, number of coins of Re 1 = 160 – 4m

Thus, by substituting the value of m, we get

Number of coins of Re 1 = 160 – (4 x 20) = 160 – 80 = 80

Now, number coins of Rs 2 = 3m

Thus, by substituting the value of m, we get

Number of coins of Rs 2 = 3m = 3 x 20 = 60

Therefore,

Number of coins of Re 1 = 80

Number of coins of Rs 2 = 60

Number of coins of Rs 5 = 20

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