Question

Madhura has Rs 5000 in denomination of Rs100 and Rs 500.If the number of

Rs100 notes is one more than twice the number of Rs500 notes, find the

number of notes of each denomination.​

Answer 1

Given:

Madhura has Rs 5000 in denomination of Rs100 and Rs 500.If the number of  Rs100 notes is one more than twice the number of Rs500 notes.​

To find:

Find the  number of notes of each denomination.​

Solution:

Let the number of Rs. 100 notes be "x"

Let the number of Rs. 500 notes be "y"

From given, we have,

The number of  Rs100 notes is one more than twice the number of Rs500 notes.​

x = 2y + 1

100x + 500y = 5000

substituting the value of x in above equation, we get,

100 (2y + 1) + 500y = 5000

200y + 100  + 500y = 5000

700y = 4900

y = 7

x = 2(7) + 1

x = 15

500 × 7 + 100 × 15 = 5000

Therefore, the  number of notes of each denomination are: 15 notes of Rs. 100 and 7 notes of Rs. 500

Answer 2

Step-by-step explanation:

Given that:

Madhura has Rs 5000 in denomination of Rs100 and Rs 500.If the number of Rs100 notes is one more than twice the number of Rs500 notes, find the number of notes of each denomination.

To find: Number of Notes of each denominations

Solution:

Let number of 100 Rs notes are x

and number of 500 Rs notes are y

Now form linear equations in two variables.

As sum of all denominations is equal to 5000 Rs

So,

$\bold{100x + 500y = 5000} \: \: \: ...eq1$

and ATQ

Number of Rs100 notes is one more than twice the number of Rs500 notes

$x - 1 = 2y \\ \\\bold{ x - 2y = 1} \: \: \: ...eq2$

Elimination Method: Multiply eq2 by 100 to equate the coefficient of x and subtract both equations

$100x + 500y = 5000 \\ 100x - 200y = 100 \\ ( - ) \: \: \: (+ ) \: \: \: \: \: \: \: \: \: \: ( - ) \\ - - - - - - - - - - - \\ 700y = 4900 \\ \\ y = \frac{4900}{700} \\ \\\bold{\red{ y = 7}}$

Put the value of y in eq2

$x - 2 \times 7 = 1 \\ \\ x = 1 + 14 \\ \\\bold{\green{ x = 15 }}$

Thus,

Madhura

100 Rs notes are 15 in number

and 500Rs notes are 7 in number.

Hope it helps you.