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Standard VII

Mathematics

Solving Equations by Undoing Operations

Kate has $ 50...

Question

Kate has $$ 500$ as currency notes in the denominations of $$ 50$ and $$ 20$ . The ratio of the number of $$ 50$ notes and $$ 20$ notes is $3 : 5$ . Then, the number of $$ 50$ notes is and the number of $$ 20$ notes is .

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Solution

Since the ratio of $$ 50$ notes and $$ 20$ notes is $3 : 5$ .
Let the number of $$ 50$ notes be $3 x$ and the number of $$ 20$ notes be $5 x$ respectively.
( $∵$ the ratio still remains the same i.e. $3 x : 5 x = 3 : 5$ ).

$(3 x) \times ($ 50) + (5 x) \times ($ 20) = $ 500$
$\Rightarrow 150 x + 100 x = 500$
$\Rightarrow 250 x = 500$

On dividing both sides of the equation by '250', we get,
$\Rightarrow \frac{250 x}{250} = \frac{500}{250}$
$\Rightarrow x = 2$

$∴$ Number of $$ 50$ notes $= 3 x = 3 \times 2 = 6$
Similarly, number of $$ 20$ notes $= 5 x = 5 \times 2 = 10$

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Kate has $ 500 as currency notes in the denominations of $ 50 and $ 20. The ratio of the number of $ 50 notes and $ 20 notes is 3:5. Then, the number of $ 50 notes is and the number of $ 20 notes is .

Kate has $$ 500$ as currency notes in the denominations of $$ 50$ and $$ 20$ . The ratio of the number of $$ 50$ notes and $$ 20$ notes is $3 : 5$ . Then, the number of $$ 50$ notes is and the number of $$ 20$ notes is .