Question

The total number of coins in a bag is 5 rupees and 10 rupees. If there are 20 backgrounds and 145 rupees, how many coins are there of 5 rupees and 10 rupees?

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Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ A bag has 5 & 10 Rupee coins

✭ There are a total of 20 coins

✭ Total amount is ₹145

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ How many coins are there of 5 & 10 Rupees?

$\displaystyle\large\underline{\sf\gray{Solution}}$

Let's assume that,

⪼ Number of 5 rupee coins as x

⪼ Number of five rupee coins will be 20-x

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

➝ $\displaystyle\sf 5x+10(20-x) = 145$

➝ $\displaystyle\sf 5x+200-10x = 145$

➝ $\displaystyle\sf -5x+200 = 145$

➝ $\displaystyle\sf -5x = 145-200$

➝ $\displaystyle\sf -5x = -55$

➝ $\displaystyle\sf x = \dfrac{-55}{-5}$

➝ $\displaystyle\sf \green{x = 11}$

Now the number of 5 rupee coins will be,

»» $\displaystyle\sf \orange{5 \ Rupee \ Coins = 11}$

Number of 10 rupee coins will be,

➳ $\displaystyle\sf 20-x$

➳ $\displaystyle\sf 20-11$

➳ $\displaystyle\sf \pink{10 \ Rupee \ Coin = 9}$

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Answer 2

Answer:

number of ₹5 coins = 11

number of ₹10 coins = 9

Step-by-step explanation:

number of ₹5 coins = x

number of ₹10 coins = y

number of backgrounds = 20

x + y = 20

y = 20 - x

total amount = 145

5x + 10y = 145

5x + 10(20 - x) = 145

5x + 200 -10x = 145

-5x + 200 = 145

-5x = 145 - 200

-5x = -55

x = 55 ÷ 5

x = 11

y = 9